# First Order Differential Equation

• December 27th 2010, 11:48 PM
winsome
First Order Differential Equation
find the general solution of the first order differential equation, t2 y’ – 2 ty = 3
• December 27th 2010, 11:50 PM
Chris L T521
Quote:

Originally Posted by winsome
find the general solution of the first order differential equation, t2 y’ – 2 ty = 3

I'm assuming you mean $t^2y^{\prime}-2ty=3$.

First note that this is the same thing as saying $y^{\prime}-\frac{2}{t}y=\frac{3}{t^2}$.

Now this is a first order linear DE. Do you know how to proceed using the integrating factor method?
• December 28th 2010, 12:20 AM
winsome
i got integrating factor of this equaiton is t^-2
is that is right ?
if yes then i m unable to get its final answer
• December 28th 2010, 12:24 AM
Prove It
Yes it's right.

So multiply both sides by the integrating factor to get

$\displaystyle t^{-2}\frac{dy}{dt} - 2t^{-3}\,y = 3t^{-4}$

$\displaystyle \frac{d}{dt}(t^{-2}y) = 3t^{-4}$.

You should be able to go from here.
• December 28th 2010, 12:31 AM
winsome
thanks
• December 29th 2010, 10:39 PM
sfhdweb
Quote:

Originally Posted by Prove It
Yes it's right.

So multiply both sides by the integrating factor to get

$\displaystyle t^{-2}\frac{dy}{dt} - 2t^{-3}\,y = 3t^{-4}$

$\displaystyle \frac{d}{dt}(t^{-2}y) = 3t^{-4}$.

You should be able to go from here.

thanks for providing solution