Differential equation Definition and 1000 Threads

Find the general solution for: $$\left(\left(x^2+y^2 \right)x-y \right)\,dx+\left(\left(x^2+y^2 \right)y+x \right)\,dy=0$$

hii, how to solve this differential equation: A*(dT(x)/dx)(1873.382+2.2111T(x))=90457.5-2.149*10^-10* (T(x))^4 where A is a constant Thank you

I have a small problem in solving a Second Order Linear Constant Coefficient Differential Equation. Please see the attached image. I understand upto the point above the arrow. What I don't understand is how he got dy/dx = 9

Please find the general solution of : $xy'-2y =x^2$

I have the differential equation: 4(2x^2 + xy) \frac{dy}{dx} = 3y^2 + 4xy The only thing I could see working is a substitution, but I can't work out which one to use. I've tried letting v = xy, or v = y/x, but neither of those seem to produce anything useful. Can anyone give me a hint?

can someone help me solve the differential equation that takes the following form? y''+Ay'+By+Cy^2=f(x), y is function of x Thanks a lot!

Homework Statement Felix, a Red bull skydiver, (mass m) who drops out of a hovering helicopter, falls long enough without a parachute(so the drag force has strenght kv2 ) to reach his first terminal velocity ( denoted v1). When his parachute opens, the air resistance force has a strenght Kv...

Homework Statement A tank containing 400 liters of water has 10 kg of salt solute (dissolved salt). Some brine containing 0.03kg/L of salt is then introduced at a rate of 2 L/min. The solution is constantly mixed and evacuated at a rate of 2L/min, such that the volume remains constant. If...

Hello MHB, I wanted to post a challange question that is hopefully not really difficult, if the question is not understandable make sure to write it so I can try explain!:)Calculate the Differential equation for $$y''+2y'=0$$ that satisfy $$\lim_{x->\infty}y(x)=1$$ and $$y(0)=0$$ Regards...

Hi All, Please I need your assistance to solve this PDE below: \frac{\partial^2 X}{\partial t^2} - \frac{\partial^2 X}{\partial z^2} + a(z,t) \frac{\partial X}{\partial t} + b(z,t) \frac{\partial X}{\partial z} +c(z,t) X =\Phi(z,t) With initial and boundary condition...

Hello MHB, $$(x^2+1)y'-2xy=x^2+1$$ if $$y(1)=\frac{\pi}{2}$$What I have done: Divide evrything by $$x^2+1$$ and we got $$y'-\frac{2xy}{x^2+1}=1$$ we got the integer factor as $$e^{^-\int\frac{2x}{x^2+1}}= e^{-ln(x^2+1)}$$ Now I get $$(e^{-ln(x^2+1)}y)'=e^{-ln(x^2+1)}$$ and this lead me to...

Homework Statement Solve the following differential equation by power series and also by an elementary method. Verify that the series solution is the power series expansion of your other solution. y'' = - 4y Homework Equations The Attempt at a Solution y'' = - 4y \\ \frac{d^{2}y}{dx^{2}}...

Hi I am trying to solve dy/dx = 3x^2-2x+2+(8/x *y) Can anyone show me how to rearrange to standard form as I am mightly confused :(

Homework Statement Find the general solution to the differential equation y'' -16y = 0, where y is a function of x. Give initial conditions that would give a unique solution to the eqution. For the differential equation y'' - k2y = R(x), with k ≠ 0 a real constant, show that it has a...

Hi! I would like to ask what is the general solution of the following differential equation \frac{\partial X_x}{\partial t} = - \frac{\partial X_t}{\partial x} Thank you very much. P.S. If you have some good resiource about this tyoe of equation to recommend please do so.

can anyone help me with MATLAB code for for solving a state homogeneous differential X=state vector Xdot(t)=AX(t)+BU(t) U is the control input i have the...

Find a solution to the following second order differential equation xy'+y=1/y^2 My Attempt: P= y'= dy/dx x dy/dx + y = 1/y^2 dy/dx + y/x = 1/xy^2 Integrating Factor = e^∫1/x dx = e^lnx y e^lnx=∫ (e^lnx)(1/xy^2) dx

Obtain the solution to the differential equation: \frac{dy}{dx} = \frac{1+y^2}{1+x^2} Multiple choice answer: a) \frac{Cx}{1-Cx} b) \frac{Cx}{1+Cx} c) \frac{C-x}{1-Cx} d) \frac{1-Cx}{x+C} e) \frac{x+C}{1-Cx} Tried integrating two sides to arrive at arctan y = arctan x + C, but not sure...

Hi folks! This one got me in doubts... Homework Statement Solve IVP (Initial Value Problem): (2xy+sin(x))dx+(x^{2}+1)dy=0, y(0)=2 Is the solution unique? Motivate why! Homework Equations Relevant equations for solving the exact equation... The Attempt at a Solution I can...

Given the following differential equation x*x''+(x')^2+y*y''+(y')^2=C where C is a constant and all differentiation is with respect to time Can i equal the first and second parts of the equation into different constants and solve separately?, meaning solving the system...

Solve the equation m\frac{d^{2}x}{dt^{2}} + c\frac{dx}{dt} + kx = (ax + b)^{2} + c^{2} for the constants m, c, k The right hand side a, b, and c are arbitrary digits. For me they are a = 2, b = 3, and c = 8. The problem recommends creating a linear system of equations for me to solve. This...

Homework Statement dy/dt = k*y*ln(y/M), where M and k are constants. Show that y = Meaekt satisfies the above equation for any constant a. Homework Equations y' = ky y = P0ekt The Attempt at a Solution Taking the derivative of y, I get: (Meaekt)*(aekt)*k which is, ky*aekt ..and I'm...

Hello! It is the first time that i write on this forum. I'm doing a PhD but i can't solve this equation: it's a non-linear second order differential equation. ay''+b|y|y'+cy+dx=0 Some ideas?

Find a particular solution for the following equation: y"+2y'+y=12.5e-t I'm not sure on which method to use. Here's my attempt using the undetermined coefficients method: →y"+2y'+y=12.5e-t r2+2r+1=0 r=-1 *not even sure if this part is useful →yp=e-t yp'=-e-t yp"=e-t...

Homework Statement y''+y= H(3pi)(t) y(0)=1 y'(0)=0 H(3pi)(t) means the heaviside function such that it is 1 above 3pi and 0 otherwise. Homework Equations The Attempt at a Solution Taking the laplace of both sides, I have that: L(y) = (L(H(3pi)(t))+s) / (s^2 + 1)...

Hi everyone, :) Continuing from http://www.mathhelpboards.com/f17/method-reduction-order-variation-parameters-4574/ thread, my friend gave me another question. He wants to check his work specifically on parts a) and d). So I will only focus on those parts. Question Summary: Given the Riccati...

Homework Statement Find the general solution for the following differential equation: y'' + x(y')^2 = 0. Homework Equations Integration, differentiation... The Attempt at a Solution Usually for these sort of DE you could use the substitution v(x) = y'(x) and this would simplify...

Hello! I'm stuck at the moment with this differential equation. I've been trying to use the method for solving these equations, but my answer is not correct according to my book. Could anyone please explain what I'm doing wrong? Thanks!

I am really confused where to start with this problem. I know about convolutions somewhat. We have done them a little. Where is a good place to begin with this problem?

Hi Everyone! I am really stuck at one differential equation: (p-y)^{2}y'(x)+(x-y)(x+y-2p)=0 where p<x<1; \ 0<y<p; \ p - parameter, 0<p<1 I have a suspicion that it does not have a solution, but is there a way to prove it mathematically in this case? I would appreciate any hints on...

Homework problem for nonlinear dynamics. Let us write xλ(t) for the solution of the initial value problem [SIZE="4"]\dot{x} = f(x) & x(0) = λ where f is continuously differentiable on the whole line and f(0) = 0. a) Find the differential equation for [SIZE="4"]\frac{∂x_{λ}}{∂λ}(t)...

Homework Statement Solve the following differential equation. y'= {{2,-1},{3,-2}}y + {{1},{-1}}(e)^{x} If it's not clear, I made an image for it. http://i.imgur.com/lypTxqf.jpg Homework Equations y{g} = y{h} + y{p} The Attempt at a Solution So basically, I am looking for...

Homework Statement differential equation (dr/dy)+r=8 ; r(1)=0.3 The Attempt at a Solution (dr/dy)=(8-r) ∫[dr/(8-r)]=∫dy ln|8-r|+c1=y+c2 ; k=c2-c1 ln|8-r|=y+k ; r(1)=0.3 then take of e^ both sides which gives 8-r=e^(y+k) 8-e^(y+k)=r and we know r(1)=0.3 which means...

dm/ds=m ; m(1)=7 when i find the diff eq ∫dm/m=∫ds ln|m|+c1=s+c2 ; k=c2-c1 ln|m|=s+k e ^ both sides m(s)=e^(s+k) ; m(1)=7 m(1)=e^(1)*e^(k)=7 i am stuck here. not sure how to proceed please help.

Homework Statement The power supply in the circuit shown has V(t) = (120V)cos(ωt), where ω = 310 rad/s. Determine the current flowing through the resistor at time t = 9.7 s, given R = 600 Ω, C = 18 mF, and I(0) = 0 A. As a reminder, Kirkhoff’s voltage law for this circuit (Eq. 8-1.3 in the book)...

Homework Statement A spherical mothball of original radius 1.2 cm slowly evaporates such that 180 days later, its radius is only 1 cm. Physically, the rate of evaporation dr/dt is proportional to the surface area of the sphere. Determine a) the time required for the radius of a new mothball to...

Homework Statement dY/dt = y(c - yb) C and B are constants. Im supposed to find and explicit solution for y, but I am having trouble. Homework Equations The Attempt at a Solution dY/y(c - yb) = dt ∫(1/c)dy/y + ∫(b/c)dY/c - yb = ∫dt (i used partial fraction decompositions)...

Hello, I am trying to solve an equation and then execute it in matlab. It is dx/dt=I(S*A*x). so I am trying to see the evolution of x with time. The variables are all in an excel spreadsheet in different columns and the name of the columns are the name of the variables. 'I' is in an...

Hi, I need help in 4 questions. I need their answers if possible.

In a video I was watching regarding how to solve these, the lecturer said that the form of a Bernoulli Differential Equation is y'+P(x)y=q(x)y^n where n>1 This means that if n = 1, it wouldn't be a Bernoulli differential equation and would be a first order linear differential equation, but if...

I understand the derivation for the simple harmonic motion equation: F = -kx ( in a 1-D case) acceleration = x''(t) = (-k/m)x so x''(t) + (k/m)x = 0 But why is the solution to this equation x = A cos (wt + ∅ ) How does one come up with this solution? I tried understanding this by reading...

Whatsup guys, im new in this forum so be easy on me... I've been banging my head against a wall lately... i have come up across a differential equation i haven't been able to resolve... does any of you know any way of resolving this equation?? a(x) needs to be differentiable for any x belonging...

Homework Statement A spring with a spring constant of 20 pounds per foot is loaded with a 10-pound weight and allowed to reach equilibrium. It is then displaced 1 foot downward and released. If the weight experiences a retarding force in pounds equal to four times the velocity at every point...

cosx(dy/dx) + ysinx = sinx cosx (dy/dx) + y/cosx = 1 e^integral (1/cosx) ? I feel like this has to do with ln again but not sure

4y'=e^(x/4) + y First I need to divide through by 4 correct? To obtain y'=(e^(x/4))/4 + (y/4) But then when I try to find integrating factor I just come up with e^(x/4) which I think is incorrect

I have the following differential equation which I obtained from Euler-Lagrange variational principle \frac{\partial}{\partial x}\left(\frac{1}{\sqrt{y}}\frac{dy}{dx}\right)=0 I also have two boundary conditions: y\left(0\right)=y_{1} and y\left(D\right)=y_{2} where D, y_{1} and y_{2} are...

I can't seem to work out this question because it's so weird The set F of all function from R to R is a vector space given the diffential equation f"(x)+3f'(x)+x^2 f(x) = sin(x) is a subspace of F? Justify your answer I know that we have to proof that it's non-empty 0. The zero vector has to...

Is there any material or book that explains how one could go from data to differential equation comprehensively? More like functional data analysis+differential equations

Homework Statement \dot{x} = -pxy + qx, \dot{y} = rxy - sy where p,q,r and s are positive constants (p does not equal r) Question is : Determine all the equilibrium points for the system of differential equations given above, expressing your answers in terms of p,q,r and s The...