# Simple ODE problem, Bernoulli's Equation

1. Sep 5, 2011

### Jonnyb42

[SOLVED] simple ODE problem, Bernoulli's Equation

1. The problem statement, all variables and given/known data

Initial value problem:

Relation: t*y' - 2*[t^2]*sqrt(y) = 4*y
Initial value: y(1) = 4

2. Relevant equations

general form of Bernoulli's equation:
y' + a(t)y = b(t)*[y^n]

First order, linear ODE form:
y' + a(t)y = b(t)

3. The attempt at a solution

My written solution. I first get Bernoulli-type equation into first order/linear form. After that I solve it with the equation y = [1/mu]*Integral[ b(t) * mu dt] (+ constant)
where mu = e^[ Integral[ a(t) dt]

I have tried this multiple times and I get the same answer. When I plug in the solution y = f(t) it does not match the differential equation, (takes some time to show.)

Any help would be great, I obviously am doing something wrong.

Last edited: Sep 6, 2011
2. Sep 5, 2011

### Jonnyb42

Well it turns out I forgot how to multiply both sides of an equation.
3rd to last step I multiply half of the right side by t^2, I'm not sure how to make this thread "solved."

3. Sep 5, 2011

### dynamicsolo

I believe you can edit the header of your own posts, so you can put a " [SOLVED] " at the end of your title.

4. Sep 6, 2011

### Jonnyb42

k thanks ill do that