# ode

1. ### Numerical methods that need a guess/approximate solutions

Hello everyone! I am currently playing with an old analog computer, which could solve time-dependent ODE/PDEs pretty fast, without time-stepping. But the problem with analog computer's solutions is that they are not very accurate. I am very curious that is there any numerical method/solver which...
2. ### Parameter for a saddle point

Hello, this is my first post here, so if I do problems, please correct me and do not be upset = ) I have one small theoretical and one greater question. small one first: 1. Homework Statement I have a potential energy : $$W(L)= -\frac{1}{4}k_4(L_x^4+L_y^4+L_z^4)$$ How can describe my potential...
3. ### Linearity in differential equations

1. Homework Statement Is the equation (x2sinx + 4y) dx + x dy=0 linear This problem also asks me to solve it, but I don't have a problem with that part. 2. Homework Equations An equation is linear if the function or its derivative are only raised to the first power and not multiplied by each...
4. ### Nonlinear Ordinary Differential Equation Help

1. Homework Statement y'=(x^2 +xy-y)/((x^2(y)) -2x^2) 2. Homework Equations 3. The Attempt at a Solution I know that really the only way to solve this one is to use an integrating factor, and make it into an exact equation. My DE teacher said that to make it into a exact equation you...
5. ### Converge pointwise with full Fourier series

I am working on a simple PDE problem on full Fourier series like this: Given this piecewise function, $f(x) = \begin{cases} e^x, &-1 \leq x \leq 0 \\ mx + b, &0 \leq x \leq 1.\\ \end{cases}$ Without computing any Fourier coefficients, find any values of $m$ and $b$, if there is any...
6. ### Checking if an equation is exact and finding the solution

1. Homework Statement Use the "mixed partials" check to see if the following differential equation is exact. If it is exact find a function F(x,y) whose differential, dF(xy) is the left hand side of the differential equation. That is, level curves F(xy)=C are solutions to the differential...
7. ### Determining the tension on a rotating particle

1. Homework Statement A particle of mass m slides (both sideways and radially) on a smooth frictionless horizontal table. It is attached to a cord that is being pulled downwards at a prescribed constant speed v by a force T (T may be varying) Use F=ma in polar coordinates to derive an...
8. ### First Order ODE

1. Homework Statement (3xy^2+4y)dx+(3x^2y+4x)dy=0 2. Homework Equations 3. The Attempt at a Solution So First I checked if both equations were exact. I took the derivative of 3xy^2+4y and also derivative of the other and they were both equal so the equation is exact. I took the...
9. ### MATLAB Matlab finite difference schemes

I have big problem with finite difference schemes (DS) on Matlab. I need write DS on Matlab, example: u_x=(u_(i+1,j)-u_(i-1,j))/2, we choose step is 1. On Matlab: u_x=(u( :,[2:n,n])-u( :,[1,1:n-1]))/2 And I can write u_y, u_xx, u_yy, u_xy. But now, I need to write for higher order, example...
10. ### Am I rewriting this differential correctly?

1. Homework Statement I have a differential equation that I need to solve numerically by writing a program. x0, y0, x_dot0, y_dot0, α are all given Hello, I have the following differential equation: http://puu.sh/d78KC/107bd6c71f.png [Broken] I want to rewrite it so I can solve it numerically...
11. ### Second Order ODE question

1. Homework Statement I'm taking an online introductory chem course, and while explaing the failure of classical mechanics to describe electron behavior, the teacher brought up the following ode which is based on newton's second law and coulombs law: -e^2/4(pi)(epsilon-nuaght)r^2=m(d^2r/dt^2)...
12. ### Differential Equations: Bernoulli Equation

1. Homework Statement Find the general solution: y'-3y=(y^2) 2. Homework Equations 3. The Attempt at a Solution divide both sides by y^2 y'(y^-2) -3(y^-1) = 1 we know v=y^(n-1) v=y^-1 v'=d/dx(y^-1) v'=-(y^-2) y' plug it back into y'(y^-2) -3(y^-1) = 1 -v'-3v=1 this is where I think...