# Simple ODE problem, Bernoulli's Equation

[SOLVED] simple ODE problem, Bernoulli's Equation

## Homework Statement

Initial value problem:

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

## Homework 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)

## 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:

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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."

dynamicsolo
Homework Helper
I'm not sure how to make this thread "solved."
I believe you can edit the header of your own posts, so you can put a " [SOLVED] " at the end of your title.

k thanks ill do that