Differential Definition and 1000 Threads

I have this basic differential equation du/dt=(u^2)*(sin t) This is obviously a separable diff eq. So what I've done is: g(t) = sin t h(u) = u^2 1/(u^2) du = sin t dt Integrating both side... 1/y = - cos t + c therefor y = - 1/(cos t + c)Which is wrong, there isn't supposed...

Homework Statement I'm stuck on Question #2 part A/B Homework Equations y'=r(1-y/k)y-h=y^2-ky+kh/r y''=2y-k Roots for y'= (k+/-sqrt(k^2-4kh/r))/2 I am assuming the positive root is y2 h<rk/4 [/B] The Attempt at a Solution on part a I'm getting the roots to be y2=(K+sqrt(k^2-4kh/r))/2 and...

Hey, I am struggling to understand what the following is in terms of the mathematics (see Nakahara page 193 at the bottom...

Homework Statement Consider the boundary value problem \begin{equation} u''(t)=-4u+3sin(t),u(0)=1,u(2)=2sin(4)+sin(2)+cos(4) \end{equation} Homework Equations Derive the linear system that arise when discretizating this problem using \begin{equation} u''(t)=\frac{u(t-h)-2u(t)+u(t+h)}{h^2}...

I can not find a solid explanation on this anywhere, so forgive me if this has been addressed already. Given something like y''+y'-(x^2)y=1 or y''+2xy'-y=x, how do I approach solving a differential with a power series solution when the differential does not equal zero? Would I solve the left...

Hello 1. Homework Statement We define the Dupin indicatrix to be the conic in TPM defined by the equation IIP(v)=1 If P is a hyperbolic point show: a. That he Dupin indicatrix is a hyperbola b/ That the asymptotes of the Dupin indicatrix are given by IIP(v)=1 , i.e., the set of asymptotic...

Homework Statement Hi,I am learning to solve 2nd-order differential eq. Suppose I have a equation dy/dx - 3x = 0...(1) Then dy/dx = 3x -----> x = 3(x^2)/2 Now if I have a 2nd order ODE such that: d^2y/dx^2 = 3....(2) Then it could be solved by integrating both sides wrt x twice,which yields y...

Homework Statement Y''-((Y')^2)+(C1*exp(Y))=C2 C1 and C2 are constants. exp = e Homework Equations No clue how to start this The Attempt at a Solution Y'=A=dY/dt Y=At+C3 (not sure) A'-(A^2)+C1exp(At+C3)-C2=0 A'-(A^2)+C1exp(C3)exp(At)=0 let C=C1*exp(C3) A'-(A^2)+Cexp(At)=0

I'm writing a paper about the projectile motion with the consideration og air resistance - I have obtained two formulas: ax = k*(vx2+vy2)0.5 * vx ay = k*(vx2+vy2)0.5 * vy - g (K and g are constants; K = -0,02, g =9,82) I cand write these two as 2 different differential equations: v'x(t) =...

Differential equation: F(y'',y',y,x)=0, y=y(x). Now, there is g=g(x) with F(g'',g',g,x)=δ, where δ is small. Then, can g(x) be taken as an approximate solution of F(y'',y',y,x)=0?

Hello, I'm struggling with a simple problem here. It asks me to solve the following initial value problem: So far I've calculated the integration factor μ(x) = ex-x2 and I multiplied both sides of the equation by it and got this...

Homework Statement Text from a classical mechanics textbook ( uploaded picture ) shows 2 diff equation describing the motion graphically presented in the uploaded picture. How were these set up? Homework EquationsThe Attempt at a Solution I don't have a slightest clue as how are these...

[ NOTE ] Thread moved to homework forums by mentor suppose in a dark room a candle is burning, so darkness increases as we move away from the candle. from the below diagram can anyone derive a differential example to show the rate of change of darkness from candle to point B. supposing...

Hey! :o Each element of the ring $\mathbb{C}[z, e^{\lambda z} \mid \lambda \in \mathbb{C}]$ is of the form $\displaystyle{\sum_{k=1}^n α_kz^{d_k}e^{β_kz}}$. A differential equation in this ring is of the form $$Ly = \sum_{k=0}^m \alpha_k y^{(k)}(z)=\sum_{l=1}^n C_lz^{d_l} e^{\beta_l z} , \ \...

Homework Statement OK, this differential equation was technically created by me, because i need to clear my doubts. Y'' + sqrt(X)*Y' + X^3*Y=3sin(x) and actually just any initial conditions as long as the solution is something i can understand, let me expand my doubt further. I've never solved...

\begin{array}{l} u = u(x,y) \\ v = v(x,y) \\ and\\ {u_x} + 4{v_y} = 0 \\ {v_x} + 9{u_y} = 0 \\ with\ the\ initial\ conditions \\ u(x,0) = 2x _(3)\\ v(x,0) = 3x _(4)\\ \end{array} Easy, u_{xx}-36u_{yy}=0 and v_{xx}-36v_{yy}=0 General solution u\left ( x,y \right )=h\left ( x+6y \right...

Homework Statement I've attached an image of the problem question, it's Q1 I'm working on This is what I have so far: we have two components of SHM, position x and velocity v. when x = 0, v = a maximum, when v = 0, x = a maximum this is represented by sin & cos functions. where x =...

#17 If you can't see the picture: Suppose that y1, y2, and y3 are solutions to a third order constant coefficient homogeneous differential equation. Suppose further that for all real t, W(y1,y2)(t)>0, but also W(y1,y2,y3)(0)=0. Then there exists c1 and c2 such that c1y1(t) + c2y2(t) =y3(t) for...

Hey! :o I want to check if there is a solution of a linear differential equation of first order in the ring of exponential sums $\text{EXP}(\mathbb{C})$. I have done the following: The general linear differential equation of first order is $$ax'(z)+bx(z)=y(z) \tag{*}$$ where $x,y \in...

Homework Statement This is a interesting (morbid) problem from Simmons- Calculus with Analytic Geometry. In a certain barbourous land, two neighbouring tribes have hated one another from time immemorial. Being barbourous peoples, their powers of belief are strong, and a solemn curse pronounced...

Homework Statement After a mass weighing 8 pounds is attached to a 5-foot spring, the spring measures 6.6 feet. The entire system is placed in a medium that offers a damping constant of one. Find the equation of motion if the mass is initially released from a point 6 inches below the...

There are two courses I can take for a Differential Equations class at my school. One is for Engineering students and is described this way (I'm a physics major fyi): This course presents an introduction to the theory of differential equations from an applied perspective. Topics include linear...

Homework Statement A circuit consists of a voltage source, voltage ##V## , a resistor, resistance ##R##, and a capacitor, capacitance ##C##, in series. (i) Show that the charge ##Q(t)## in the capacitor satisfies the equation ##R Q' (t) + Q(t)/C = V ##. (ii) Suppose that ##R##, ##C## and...

Homework Statement We have the equation ## (\frac{dr}{ds})^2+(\frac{l}{r})^2=1 ## and want to solve to get ## r=\sqrt{l^2+(s-s_0)^2}## Homework EquationsThe Attempt at a Solution I have worked backwards, plugging in the solution to prove that it is correct, but the closest I have gotten to...

Homework Statement A uniform 10-foot-long heavy rope is coiled loosely on the ground. One end of the rope is pulled vertically upward by means of a constant force of 5lb. The rope weighs 1lb/ft. Use Newton's second law to determine a differential equation for the height x(t) of the end above...

Homework Statement Chemical reactions being studied in which a body A undergoes transformations according to the following scheme: http://prntscr.com/8shuvb k1, k2, k3 , k4 are the rate constants . We denote x (t ), y ( t) , z (t) the respective concentrations of the products A, B, C at a...

Homework Statement Water with a small salt content (5 lb in 1000 gal) is flowing into a very salty lake at the rate of 4 · 105 gal per hr. The salty water is flowing out at the rate of 105 gal per hr. If at some time (say t = 0) the volume of the lake is 109 gal, and its salt content is 107...

Hey guys, I have a question concerning the rewriting of a differential equation solution. In the example above, they rewrite [y=(plus/minus)e^c*sqrt(x^2+4)] as [y=C*sqrt(x^2+4)]. I understand that the general solution we get as a result represents all the possible functions, but if we were to...

Hi, I am struggling to find the solution to the following equation. I can't account for the exponential term, so clearly something is going wrong... 1. Homework Statement Find the general solution to ##x' = tx + 6te^{-t^2}## where ##x(t)##. Homework EquationsThe Attempt at a Solution [/B]...

Hey! :o I want to check if we can always find a solution of a linear differential equation of first order in the polynomial ring $F[z]$. I have done the following: The general linear differential equation of first order is $$ax'(z)+bx(z)=y(z)$$ where $x,y \in F[z]$. Or is it possible that...

Homework Statement So there is a falling object, you have to take into account the boyant force, the pull of gravity and the drag force A time dependent distance equation is what we're looking for Homework Equations Fd=CdApav2/2 Where Fd is the drag force Cd is the drag coefficient A is the...

Homework Statement I am reading a note on differential equation.There is a point that I don't understand,hopefully someone can explain (Please see the attched) Homework EquationsThe Attempt at a Solution The notes wrote " a1t + b1 x + c1 = a1T + b1X a2t + b2t + c2...

Let the PDE $u_{xx}-4u_{xy}+4u_{yy}=0.$ Reduce to the canonical form.Good Morning MHB :). My problem is find the canonical form of the PDE know an variable change. But how I can transform the equation? Thanks.

Please help me solve this differential equation for the initial condition (0,-1): dx/dy = ((1+x^2)^(1/2))/(xy^3) I think I'm doing something wrong because I end up with ((x^2)(y^3))/2 = ((x^2)+y)^(1/2) + c, but when plugging in the initial condition it ends up being the square root of...

Homework Statement (4x^3y^3-2xy)dx+(3x^4y^2-x^2)dy=0[/B]Homework Equations (4x^3y^3-2xy)dx+(3x^4y^2-x^2)dy=0 The Attempt at a Solution i expanded it as 4x^3y^3dx-2xydx+3x^4y^2dy-x^2dy=0 next we have to take the common such that there will be m(X)(xdy+ydx)[/B] m(x) is the common onee

$y(x^3e^{xy}-y) \, dx+x(xy+x^3e^{xy}) \, dy=0$ change it into exact differential and help me in solving it

Homework Statement I think there may be something wrong with a problem I'm doing for homework. The problem is: Solve the IVP with the differential operator method: [D^2 + 5D + 6D], y(0) = 2, y'(0) = \beta > 0 a) Determine the coordinates (t_m,y_m) of the maximum point of the solution as a...

Hi, I'm currently studying to become a chemical engineer. After learning differential equation and linear algebra, I've realized how useful they are in my engineering courses since they make setting up equations and solving them so much easier. So I was wondering if there are other math that...

1. Homework Statement It's to do with mirages, but I don't think the physics context is too important. It's also possible that the solution doesn't involve differential equations, and my method is completely wrong. I've been given that: ##A = \frac{n(1+ay)}{ sqrt(1+(y')^2)}## where y' is...

Homework Statement Hi there. I have a simple RC circuit with a battery voltage of 10 V, R = 1 Ω, C = 1 F and a switch. I want to use the Explicit Euler (forward divided difference) to solve the equation and check for stability, rather than using a ODE. I am finding the equation for when the...

Homework Statement Hi, basically I have a boundary value problem and just want to check that my general solution is correct. x'''' + 16x = 0 Homework EquationsThe Attempt at a Solution I'm pretty sure you make a characteristic equation which would be m4 + 16 = 0. Solving this I get m to be...

Euler mentions in his preface of the book "Foundations of Differential Calculus" (Translated version of Blanton): I don't understand here, who/who all had invented/discovered the study-of-ultimate ratio (differential calculus) for rational functions long before (Newton and Leibniz), without...

Hi evry body i would like to have an help to resolve this exercice below the followin differential equation with its initial condition dy/dt=-lambda t y(t) t>=0 avec y(0)=y0 where lambda is damping coeficient strictly positive. -find the solution of this equation with Euler's explicite and...

Homework Statement Given u(x.y), find the exact differential equation du = 0. What sort of curves are the solution curves u(x,y) = constant? (These are called the level curves of u). u = cos(x2 - y2)The Attempt at a Solution partial derivative du/dx = (-2x)sin(x2 - y2)dx partial derivative...

Homework Statement A simple electrical circuit consists of a voltage source E(t) = t*e-t volts, a resistor R = 1 and an inductor L = 1/10 H connected in series. It is assumed that I(0) = -10/81 a) The differential equation that governs the current I (t) in this circuit . b) Find the time...

Homework Statement equation (1) y' + (ylny)/x = xy we set y(x)= eu(x) Equation (1 ) proposed becomes an equation 1st order linear differential type : equation (2) u ' + p( x) u = q ( x) a) Find the equation ( 2) using the change of variable proposed above. Homework EquationsThe Attempt at a...

Euler was the master in analysisng anything. This can be seen in his words in the preface of his book "Mmathematica" (translated by Ian Bruce), where he speaks on the text of Hermann "Phoronomiam": Euler has given many insightful words on analysisng things in his preface of many other books...

Homework Statement A block of mass m, which has an initial velocity v0 at time t = 0, slides on a horizontal surface. If the sliding friction force f exerted on the block by the surface is directly proportional to its velocity (that is, f = -kv), A) Write a differential equation for the...

Homework Statement Find the general solution to the equation. Homework Equations (dy/dx) - y - e^3x=0 The Attempt at a Solution [/B] I rewrote this as dy/dx - y = e^3x This is a linear first order ODE, in the form dy/dx + P(x)y = f(x) P(x) = 1; f(x) = e^3x The integrating factor =...

So I'm not sure whether this should be posted in the Physics forum or not, but here goes: I'm a Junior ME student at NC State taking a Vibrations course. We've gone over the general differential equation for mass-damper-spring systems where Meq⋅x'' + Ceq⋅x' + keq⋅x = Fextermal What I was...