# Thread: Differential equations

1. ## Differential equations

Solve:
$x^2\frac{d^2 y}{dx^2} + 2x\frac{dy}{dx} = \frac{1}{X^2}$
and i am very stuck .
Can i integrate the whole thing? But im unsure as to what you get because of the coefficients...
Then Dividing by the coefficients doesnt offer me much help either lol =(
Thanks.

2. Originally Posted by AshleyT
Solve:
$x^2\frac{d^2 y}{dx^2} + 2x\frac{dy}{dx} = \frac{1}{X^2}$
and i am very stuck .
Can i integrate the whole thing? But im unsure as to what you get because of the coefficients...
Then Dividing by the coefficients doesnt offer me much help either lol =(
Thanks.
I'm just starting my study of differential equations; however, I think that I can help. This equation looks like the derivative of a product. Y= -1/2*x^-2 - c*x^-1 +c

3. Originally Posted by Bilbo Baggins
I'm just starting my study of differential equations; however, I think that I can help. This equation looks like the derivative of a product. Y= -1/2*x^-2 - c*x^-1 +c
Hmm, did you have to find that by guessing?

4. Originally Posted by AshleyT
Solve:
$x^2\frac{d^2 y}{dx^2} + 2x\frac{dy}{dx} = \frac{1}{X^2}$
and i am very stuck .
Can i integrate the whole thing? But im unsure as to what you get because of the coefficients...
Then Dividing by the coefficients doesnt offer me much help either lol =(
Thanks.
You'll notice there's no $y$ is this problem so it you let

$u = \frac{dy}{dx},\;\;\; \text{then}\;\;\; \frac{du}{dx} = \frac{d^2 y}{dx^2}$

and your problem becomes

$x^2 \frac{du}{dx} + 2x u = \frac{1}{x^2}$ linear!

5. Originally Posted by AshleyT
Hmm, did you have to find that by guessing?
No, not at all. I just saw it. The derivative of a product is pretty conspicuous.

6. Originally Posted by Bilbo Baggins
No, not at all. I just saw it. The derivative of a product is pretty conspicuous.
Oh ok, thanks =)