Differential equation Definition and 1000 Threads

Homework Statement Show that a solution to y'=y(6-y) has a an inflection point at y=3. The Attempt at a Solution If y has an inflection point, then y''=0. I know that y'=y(6-y), and therefore i know that y''=(y(6-y))'=(6y-y2)'=6-2y So, if y''=0, and y''=6-2y then 0=6-2y => y=3. Solved. But...

Is it possible to solve a differential equation of the following form? $$\partial_x^2y + \delta(x) \partial_x y + y= 0$$ where ##\delta(x)## is the dirac delta function. I need the solution for periodic boundary conditions from ##-\pi## to ##\pi##. I've realized that I can solve this for some...

This is question 1.4 of Chapter 8 of Mary L. Boas's Mathematical Methods in the Physical Sciences, Edition 2. I'm using it as a substitute for my ordinary differential equations class since my textbook has apparently been lost somewhere in the mail. Homework Statement Find the distance...

please provide step by step method to solve this 2nd order non linear differential equation: attached with this thread. take FUCOS(Ѡt) and FUsin(Ѡt) as zero.

Hello! This is my first post to this excellent forum! I would like some help with this exercise: u_{xx} (x,y) + u_{yy} (x,y) = 0, with 0 < x < 2 \pi , 0 < y < 4 \pi u_x (0,y) = 0, \, u_x(2 \pi, y) = 0, \, 0< y < 4 \pi u(x,0) = a \cos(2x), \, u(x, 4 \pi) = a \cos^3(x), \, 0<x<2\pi...

I want to be able to map the position of a planet given initial position, velocity, and acceleration. I know the equation for Gravitational force (Newtonian) is: F=-GMm/r^2 Using Newtons second law this gives: m(d^2x/dt^2)=-GMm/x^2 Then simple Algebra yields: (d^2x/dt^2)+GM/x^2=0 I...

Homework Statement Obtain the differential equation of the family of plane curves described: Circles tangent to the x-axis. Homework Equations (x-h)^2 + (y-k)^2 = r^2 The Attempt at a Solution I tried to answer this question using the same way I did on a problem very similar to this...

Hi, I desperately need help to solve the following differential equation for buckling of a beam with a uniform axially applied force and a point force: ∂y(x)2/∂x2+(P+Q.x).y(x)=0 Where P and Q are constants. P is known and Q is the critical axial uniform force (N/mm) that will cause...

Homework Statement Solve PDE ##\frac{\partial u}{\partial t}-k\frac{\partial^2 u}{\partial x^2}=0## for ##0\leq x \leq \pi ## and ##t\geq 0##. Also ##\frac{\partial u}{\partial x}(0,t)=\frac{\partial u}{\partial t}(\pi ,t)=0## and ##u(x,0)=sin(x)##.Homework Equations The Attempt at a Solution...

With some help in this other thread http://mathhelpboards.com/calculus-10/differiental-equation-question-particular-solutions-10864.html I was able to see what I was doing wrong. Now I'm going to apply it to a different problem and see if I'm doing it right. dy/dx+(3/x)y=-16sin x^4, y(1)=1...

Still learning the formatting commands, sorry! I'm aware of the $(dy/dx) + P(x)y=Q(x)$ formula, as well as the $e^{\int P(x) dx}$ formula needed to get the "I" factor. Here's the equation. $$(dy/dx)+(2/x)y=3x-5$$ The "$P(x)$" would be $(2/x), \int 2/x\ dx = 2 \ln(x), e^{2 \ln(x)} = x^2$, so...

Verify that given function is a solution. y'' - 2y' + 2y = 0 , y=e^x(Acos x + Bsin x) First I take derivative of y which is y+e^x(-Asin x + B cos x) then I asign e^x(-Asin x + B cos x) to y'-y. Then I take derivative of y' which is y'+(y'-y)-y which equals 2y'-2y=y'' then I use y'' as...

There is differential equation with initial condition perplexing me. y'+ y = 1, y = ce^-x + 1 , y = 2.5 when x = 0 First I take derivative of y which is -ce^-x then I sum it up with y which is -ce^-x+ce^-x + 1 equals 1 which is in harmony with y' + y = 1 but it seems that this is...

Homework Statement We have given coordinates on the Earth from where we are shooting to the Moon (bullet has really small mass). The Moon orbit and therefore Moon position in time t is known. The task is to compute the initial velocity vector (the angle and velocity of the bullet), so the...

Homework Statement Hello I am new to this forum, but I hope I can get help with a problem I haven't been able to figure out what to do with. info: we have a one dimensional equation -d/dx [a(x) du/dx] = p(x) where we seek a solution u(x) where x is within [0,1] , that satisfies...

I have a differential equation y'' + y' -2y = 3e-2x + 5cosx y = yc + yp I found yc = Ae-2x + Bex for A, B arb. Const. Then when selecting a trial function to find the particular integral, yp I came up with: yp = ae-2x + bcosx + csinx However the correct trial function...

Homework Statement I have a differential equation: \ddot{x} -2\dot{x} + 5x= 10 + 13cos(3t)Homework Equations x(t) = xc + xp where xc is the Complementary Function and xp is the Particular Integral.The Attempt at a Solution I have formed and solved the auxiliary equation: m^{2} - 2m + 5 = 0...

Homework Statement We are given a 2 dimensional space time line element and we want to calculate the light cone at a point (x,y) Homework Equations ds^2=x(dy)^2-2(dy)(dx) The Attempt at a Solution For a light cone, ds^2=0 so x(dy)^2-2(dy)(dx)=0 now what?

Why is it assumed that the method of separation of variables works when the boundary conditions of some boundary valued problem are homogeneous? What is the reasoning behind it?

Homework Statement d^2x/dt^2 - 3 dx/dt + 2x= 2e^3t give that at t=0, x=5, and dx/dt=7 Homework Equations i can't figure out how to derive the values of A, B, and C from the attempted equation solution. please help me out here. thanks The Attempt at a Solution

how can we solve this differential equation? (ax+y)∂f/∂x + (ay+x)∂f/∂y =0 with this condition: if a=0 then f(x,y)=x^2 - y^2

1. http://i.imgur.com/3xya7IM.jpg 3. I curently do not understand how to jump to finding an acceleration due to gravity (in those terms asked) from the differential equations

Homework Statement for this question, i sub u=xy and try to eliminate y in my working.. but how should i proceed since the term ux cannot be separated Homework Equations The Attempt at a Solution

A second order differential equation form d2y/dx2 = f(x,y,dx/dy) How do I read the language on the right hand side?

Homework Statement i got stucked here. below is the answer given. can anybody help please? Homework Equations The Attempt at a Solution

Homework Statement Solve (1+bx)y''(x)-ay(x)=0Homework Equations The Attempt at a Solution I'm used to solving homogeneous linear ODE's where you form a characteristic equation and solve that way, here there is the function of x (1+bx) so how does that change things?

Homework Statement \frac{du}{dt} = e^{5u + 7t} Solve the separable differential equation for u: Use the following initial condition: u(0) = 6. The Attempt at a Solution I tried to take the natural log of each side but now I'm stuck. How can I separate the equation when both the u...

Homework Statement I would like to solve a 2nd Order Differential Equation using the Improved Euler Method. The 2nd ODE is a Mass-Spring-Damper equation. I tried coming up with an solution for the Improved Euler Method, but not entirely sure. Can you help me and have a look if this is correct...

Homework Statement Solve ##y^{''}+zy=0## where ##y(0)=0## and ##y^{'}(0)=1##Homework Equations ##y(z)=z^r\sum _{k=0}^{\infty } C_kz^k## The Attempt at a Solution Well firstly: ##r(r-1)+p_0r+q_0=0## where obviously ##p_0=q_0=0## so ##r_1=0## and ##r_2=1##. In general ##y(z)=\sum...

Homework Statement {g}'\left ( s \right )+\mu g\left ( s \right )={f}'\left ( -s \right )+\mu f\left ( -s \right ) Integrate up to get g\left ( s \right )=-f\left ( -s \right )+2\mu e^{-\mu s}\int_{-s}^{\infty }e^{-\mu {s}'}f\left ( {s}' \right )d{s}' Homework Equations As above...

Homework Statement Solve: $$\frac{\delta F[f]}{\delta f(x)}=b(x)f(x)^2F[f]$$ For b(x) a fixed smooth function. Homework Equations $$\left.\frac{dF[f+\tau h]}{d\tau}\right|_{\tau=0}\equiv \int\frac{\delta F[f]}{\delta f(x)}h(x)dx$$ The Attempt at a Solution This isn't a homework problem...

Hello, I have trouble solving the following differential equation. I am trying to learn how to solve that form of DEs. The DE is: x2*dy/dx = y2 There are no initial-value problem, but the solution should be given such that y is defined for all x. The most important for me is to...

Hello I was recently working on a problem where I had to solve the differential equation in the title ( where y is a function of t), I found an exact series solution through peturbation theory in which a pattern emerged between successive orders. However, the series solution is not very useful...

Consider non-dimensional equation for the height at the highest point is given by \begin{equation} h(\mu)= \frac{1}{\mu}- \frac{1}{\mu^2} \log_e(1+\mu) \end{equation} $0<\mu\ll 1.$ Determine to $O(\mu)$, the (non-dimensional) time for the body to travel from the highest point to the ground, and...

A body of constant mass is thrown vertically upwards from the ground. It can be shown that the appropriate non-dimensional differential equation for the height x(t;u), reached at time t\geq0 is given by \begin{equation} \frac{d^2x}{dt^2} = -1-\mu (\frac{dx}{dt}) \end{equation} with...

A body of constant mass is thrown vertically upwards from the ground. It can be shown that the appropriate non-dimensional differential equation for the height $x(t;u)$, reached at time $t\geq0$ is given by \begin{equation} \frac{d^2x}{dt^2} = -1-\mu (\frac{dx}{dt}) \end{equation} with...

Homework Statement Hi everyone, I'm currently studying an online course on climate science and am a bit overwhelmed by the calculus. I have studied calculus to second year of college but that was a while ago and I'm very rusty. A few weeks ago I was a question to find the how long it would...

Homework Statement (x2)d2y/dx2 + 2*x*(dy/dx) + w2*x2*y=0 Where w is a constant Homework Equations The Attempt at a Solution I am having a really hard time figuring out how to solve this. Usually for second order linear ODEs I start with assuming a solution of form y=eλx...

Homework Statement for this question , i 've got my positive 9 but i got -64 , can anyone tell me which part is wrong? Question : https://www.flickr.com/photos/123101...3/13907725466/ Wroking : https://www.flickr.com/photos/123101...n/photostream/ Homework Equations The...

i got k = ln |9/64| then how can the next step using ln 0 doesn't make sense. what should i do?

When I multiply out the first line I end up with an extra (dA/dx)*(dσ/dx). Can someone please show me how i get from the first line to the second. Thanks

Homework Statement I managed to work this problem all the way through, but I am in no way certain of my answer. I'd greatly appreciate any insight! Find the solution of the initial value problem. y'''+4y'=x, y(0)=y'(0)=0, y''(0)=1 Homework Equations Just for clarification...

I have a differential equation to solve below on the motion of an object oscillating in water with a restoring force equal to -Aρgx and a damping force equal to -kv^2. ma+kv^2+Aρgx=0 K, A, ρ and g are constants and I need to solve the equation for x. a (acceleration). v (velocity). x...

The nonlinear oscillator y'' + f(y)=0 is equivalent to the Simple harmonic motion: y'= -z , z'= f(y) the modified Symplectic Euler equation are y'=-z+\frac {1}{2} hf(y) y'=f(y)+\frac {1}{2} hf_y z and deduce that the coresponding approximate solution lie on the family of curves...

Homework Statement I am trying to model using differential equations rain falling from the sky, hitting the pavement, and then running off the pavement into the ground. I'm a little rusty on differential equations and I'm just wondering if my answer is correct. In this model I'm assuming that...

Show that the explicit Runge-Kutta scheme \begin{equation} \frac {y_{n+1} -y_{n}}{h}= \frac{1}{2} [f(t,y_{n} + f(t+h, y_{n}+hk_{1})] \end{equation} where $k_{1} = f(t,y_{n})$ applied to the equation $y'= y(1-y)$ has two spurious fixed points if $h>2$. Briefy describe how you would...

Hey! :o I have to find the Normal form of the 2.order partial differential equation. I am not sure if my solution is correct.. The differential equation is: $ u_{xx}-4u_{xy}+4_{yy}-6u_x+12u_y-9u=0$ $a=1, b=-2, c=4$ $b^2-ac=4-4=0 \Rightarrow $ parabolic $\frac{dy}{dx}=\frac{1}{a}(b \pm...

I have, as is normal for anyone working in physics, come across a differential equation describing the system I am looking it. Now I know little about solving partial differential equations, and indeed I am not even sure if an analytical solutions exists for my equation, but here it is anyways...

Hey! :o I have the following exercise: Write in the normal form the differential equation $$u_{xx}+\frac{2y}{x}u_{xy}+\frac{y^2}{x^2}[(1+y^2)u_{yy}+2yu_y]=0$$ Hint: You can suppose that the one new variable is given by $\xi=x$ I have done the following: $a=1, b=\frac{y}{x}...

Homework Statement Solve ##y''+y-sinx=0##. Homework Equations The Attempt at a Solution I am actually working on variational problems which brought me to this differential equation. I thought that taking ##y=Asinx+Bcosx## would solve it, yet it does nothing useful. In other...