Differential equation Definition and 1000 Threads

Hello MHB, solve this system of linear differential equation $$f'=f-g-h$$ $$g'=-f+g-h$$ $$h'=-f+g+h$$ with boundary conditions $$f(0)=1$$, $$g(0)=2$$ and $$h(0)=0$$ we get that $$\lambda=1$$ and $$\lambda=0$$ now for eigenvector or we can call it basis for eigenvector $$\lambda=0$$ i get Is...

Hello, can you guys help me please with this differential equation from Demidovitch book, is to find the solution transforming to polar coordinates :

I need to prove that the solution of this differential equation: dx/dt = -x3 + 2*x + sin3(2*pi*t) - 2*sin(2*pi*t) + 2*pi*sin(2*pi*t) has the solution: ψ(t,0,0) = sin(2*pi*t) I know that I need to get all of the x's on one side and the t's on the other then integrate, but I can't...

Homework Statement Suppose that a fourth order differential equation has a solution y=-9e^(3x)xcos(x). a. Find such differential equation, assuming that it is homogeneous and has constant coefficients. b. Find the general solution to this differential equation. x is the independent...

I am trying to write out a differential equation for the Wien bridge oscillator circuit. I have attached a picture of the circuit. I am considering ideal conditions. I am trying to solve for the output voltage but I need help setting up the differential equation.

Homework Statement Problem 5 on the attached Sheet here Homework Equations We studied the Power Series Method and how to calculate a linearly independent solution if one solution is already known. So we need to find one solution (probably) using the power series method and then using...

Problem: Newton's 2nd Law for rotational motion states that the product of the moment of Inertia, I, and the angular acceleration alpha(t) is equal to the net Torque acting on a rotating body. Consider a wheel that is being turned by a motor that exerts a constant torque T. Friction provides...

Homework Statement Find the general solution to the following differential equation. dy/dx = 2x( (y^2) + 1) Homework Equations The Attempt at a Solution I got all x terms on one side and all y terms on the otherside 2x dx = 1/( (y^2) + 1`)dy integrate x^2 + c =...

Homework Statement dx/dt=x+y dy/dt=-y+8x Solve this system useing Eulers method or by elimination method. Homework Equations Eulers method I know that in general I should look for solution in form y=const*exp[kx] z=const2*exp[kx] But in my case I am not sure if i can write...

Homework Statement Solve y' = (y^3)(t^2) for the initial condition y(0)=0 and state in which interval in 't' this solution exists. The Attempt at a Solution First I divided both sides by y^3 and then subtracted t^2 from each as well, -t^2 + y'(y^-3) = 0 then solved, (-t^3)/3 +...

If we have \frac{1}{X(x)} \frac{d^2 X}{dx^2}=-κ^2, the literature is saying that the solution must be: e^(±iκx), but am always getting e^(±k^2x). Isn't the approach is to decently integrate twice and then raise the ln by the exponential? Where am I going wrong? Thanks

Homework Statement f(x,y)= 3x5y2 - 30x3y2 + 60xy2 +150 How do I find the critical points where this equation equals zero? Homework Equations None? The Attempt at a Solution I found the partial derivatives, but I'm stuck now and don't know where to go from here. dx = 15x4y2...

Determine a region of the xy-plane for which the given differential equation would have a unique solution whose graph passes through a point (x_0, y_0) in the region. x \frac{dy}{dx} = y What does an xy-plane have to do with anything? I looked up the definition of unique solutions and here it...

Make up a differential equation that does not possesses any real solutions. step 1)consider the definition of solution Any function \phi defined on an interval I and possessing at least n derivatives that are continuous on I which when substituted into an nth-order ordinary differential...

Verify the indicated function y=phi(x) is an explicit solution of the given equation. Consider the phi function as a solution of the differential equation and give at lease one interval I of definition. (y-x)y'=y-x+8 where y=x+4\sqrt{x+2} So the derivative is y'=1+\frac{2}{\sqrt{x+2}} and the...

Homework Statement It's been a long time since I've done DE's and now I'm stuck with a monster of this form: y'(t) = a*g'(t) + b*g(t) + c*y(t) where g(t) is a known function and a, b and c are constants. What kind of DE is this, and how can I solve for y(t) -- or better yet, what...

Homework Statement What are the bifurcation values for the equation: dy/dt = y^3 +ay^2 Homework Equations The Attempt at a Solution Equilibrium solutions: y^3 + ay^2 = 0 ==> y^2 (y + a) = 0 ==> y = 0 (double root), or y = -a. a = 0 is the sole bifurcation point, since...

Homework Statement Using Euler's Method: a) Find the approximate values of the solution of the given initial value problem at t = 0.1, 0.2, 0.3, and 0.4 using the Euler method with h= 0.1 b) Repeat part (a) with h = 0.05. I am doing part (b). The function is y' = 0.5 - t + 2y...

Hello I seek solutions of differential equation x3y′′(x)+(ax3+bx2+cx+d)y(x)=0 thank you

y'''-5y''+6y'=8+2sinx If I let w=y', would I be able to solve this differential equation? I'm currently stuck and I just want to know if making this substitution is why I am stuck.

I cannot figure out where I am going wrong. My answer and the textbook answer are different by a negative sign. Can someone review my work and tell me what I am doing wrong?

Hi guys! I am really stuck at quite a complicated (from my point of view) differential equation. I would really appreciate any hints or suggestions on how to tackle and solve it if it is possible, thanks...

Homework Statement Solve the separable differential equation for u du/dt=e^(5u+2t) Use the following initial condition: u(0)=13 The Attempt at a Solution Honestly I didn't get very far on this one. I took the natural log of both sides, ln du/dt = 5u+2t And now I am stuck. Should I divide...

1. Find a differential equation with the solution y(x) = (x + C)3 The answer cannot contain C) 2. There are no relevant equations. 3. I'm not entirely sure how to do this; I understand that a differential equation has multiple solutions, but for some reason I'm lost on how to find...

how do i find the yk value?? the k, tk and mk values makes sense to me Problem #1: http://imageshack.us/photo/my-images/14/fe0x.jpg/ Solution manual: http://imageshack.us/photo/my-images/5/hu55.jpg/

Homework Statement y = c1e3xcos(2x)+c2e3xsin(2x)+c3+c4x Homework Equations Differential Equations. The Attempt at a Solution I am having trouble what the roots are for the c3, and c4 parts. I know they are a repeated root, but is it just k= 0? It seems like it would work, but I...

Homework Statement y = c1e3x+c2xe3x+c3e2xsin(x)+c4e2xcos(x) Homework Equations Differential Equations. The Attempt at a Solution I have the roots of k=3, k=3, k=2+i, k=2-i. Now I am just stuck on how to put the roots together to get the original equation. I am just stuck on the complex...

Hi I am working on a problem that ends up having the natural log of a negative e which I'm confused on how to find the explicit solution. The Problem: Find an explicit solution with C. y'-e^{-y}cos(x)=0 My Conclusion: First of all, I'm confused how I should solve this explicitly if I'm...

Homework Statement Find the input/output differential equation for the LRC circuit in the given figure. The figure is shown in the attachment. Homework Equations V(t) = Ri(t) For inductor, v(t) = Ldi(t)/dt I(t) = 1/L∫v(λ)dλ For capacitor, dv(t)/dt = i(t)/C v(t) = 1/C∫i(λ)dλ...

I have the differential equation \frac{dM}{dt}=4\pi \rho(r,t)r(t)^2\frac{dr}{dt} which is the first term from M(t)=4\pi\int_0^{r(t)}C(r,t)r(t)^2dr This describes the change in mass (M) of a sphere from a change in radius (r) given a density (rho) that depends on radius and time (t). My...

The mass of a sphere with density as a function of radius is M=4\pi \int_0^r\rho(r) r^2dr Lets say the radius increases and decreases as a function of time t. So: M(t)=4\pi \int_{0}^{r(t)}\rho (r) r(t)^2dr I want to know the basic equation describing the mass added or removed...

Homework Statement Obtain the solution of the differential equation x'' + w2nx = t My use of L refers to the Laplace Homework Equations The Attempt at a Solution L{x'' + w2nx = t} I decided to do the Laplace of each part individually starting with x'' L{x''} =...

Homework Statement Solve the following differential equation: Homework Equations 2 y (y'')^2 + 2 y y''' y' -2 (y')^2 y'' = - (y')^2 The Attempt at a Solution I don't know if the following is useful, but if you divide both sides by y^2, the LHS of the above becomes: (2 y...

Homework Statement Hello everybody :) Now, I have a differential equation to solve. Its a Bernoulli's type of eq. Homework Equations (2x2lny-x)y' = y The Attempt at a Solution I tried of putting it in this way: y'/y = 1/2x2lny-x and then considerin z=1/y, but it doesn't seem...

Homework Statement dL/dp = L/2, L(0) = 100. Find the solution to the differential equation, subject to the given initial condition. My textbook says the answer is L = 100ep/2, but I don't know how to get that answer (or e for that matter). Homework Equations ? The Attempt at a...

Homework Statement y' + 3y = t + exp(2t)Homework Equations The Attempt at a Solution My solution is y = t/3 + exp(-2t) -1/9 + c. The solution in the back of the book is y = cexp(-3t) + (t/3) - (1/9) + exp(-2t). How come the two solutions differ so vastly? I followed the procedure outlined in...

i tried to solve this question in all the ways i knew but it wouldn't work ..please help xy^2dy/dx + y = x^2 i tried to solve it by using linear first order differential equation technique and also by using different exact and reducable exact differential equaions... help me

Homework Statement t^2y" + 5ty' + 4y = 0 Possible solutions: y_1(t) = t^{-2} and y_2(t) = t^{-2} lntHomework Equations The Attempt at a Solution I was able to verify that y_1 was a solution, by the substituting the function, and its derivatives, into the differential equation, which...

The differential equation: y' -2ty = 1. The possible solution: y=e^{t^2} \int^6_0e^{-s^2}ds + e^{t^2}. For the integral, I employed integration by parts: Let u=e^{-s^2} \rightarrow du = -s2e^{-s^2}ds and Let dv = ds \rightarrow v=s. This lead to: [se^{-s^2}|^t_0 - \int_0^t...

I'm going to be taking a course in differential equations and I'm nervous. From previous calculus courses I know the derivative is the ratio of how one quantity changes with respect to another the integral is the area under the curve So what's a differential equation? According to here "A...

Dear All, Recently, I have measured a series of nonlinear vibrational spectra from which I would like to extract some useful information about kinetics of the exchange process occurring in the studied system. I need to fit my experimental data to kinetic model that is a solution of coupled...

Homework Statement Find the ODE of the following (1) du/dy = -u (2) d^2u/dxdy = -du/dx Homework Equations For question 1, the answer is u= A(x)e^(-y) while for question 2, the answer is u= e^(-y)(B(X) + c(Y)) The Attempt at a Solution I've already solved the question, but...

Hi. Let me preface this by saying that I know nothing about economics. However, I learned a little bit about the concept of price elasticity of demand (that for something really elastic, if price goes up a little, demand will go down a lot), and I came across an equation relating price, demand...

Sorry I couldn't think of any more relevant title. Here's the equation: {x^2} - 3{y^2} + 6xy\frac{{dy}}{{dx}} = 0 I'm thinking of rewriting the above to \frac{{dy}}{{dx}} = \frac{{3{y^2} - {x^2}}}{{6xy}} followed by a change of variable u=y/x. But should I rule out the case when either x=0 or...

Trying to make a calculation and I ran into the following diff equation: r''=a+b/r^2 And I can't seem to remember how one would go about solving it. b = 1355041.84 r(0) = 1400 r(t) = 239.6 r'(o) = 0 r'(t) = 75.2 a = ? I'm specifically looking to find the value of the constant a...

I'm trying to find the equilibrium size of a planetesimal which is made of a material whose density is pressure dependent. (quite a mouthful) I have to solve this differential equation: y(x^2y''+2xy')+2y^2+bxy'=ax^2y^3+(xy')^2+by where a and b are constants.

Hey guys, I have a question for you... how would one go about solving an equation like this... or this... This came across my mind the other day. I was wondering how to solve that equation if the function is of t-1, instead of t. Obviously, if it was f(t), the solution would be Ce^t, but I was...

So, as a result of a thought experiment, I've got a differential equation, which I can't solve: R r'' \sin \frac{r}{R} - 2 (r')^2 \cos \frac{r}{R} - R^2 \cos \frac{r}{R} \sin^2 \frac{r}{R} = 0 , R > 0 To make the matters worse, the function r(\varphi) will probably depend on multiple...

Hello, I am new here. I hope I am posting my problem at the right place. I need some urgent help regarding the following differential equation: A\frac{d^{2}y}{dx^{2}}+B\frac{dy}{dx}=f(x,\lambda)...(1) where, A and B are constants. x and \lambda are independent. I have solved...

hello ... I wanted to demonstrate the solution of a differential equation, and as I do not yet know the latex language, then I take pictures of the leaves with my solutions ... the user who wants to give more solutions is well received and is welcome ... att jefferson alexander vitola (Smile)...