Solve Differential equation for the original equation

• Feb 21st 2011, 11:17 AM
sparky
Solve Differential equation for the original equation
Hi,

Is my working correct for the following question?

Question: Solve for the following differential equation for the original equation: $$\frac{dy}{dx} = \frac{-x}{2y}$$

Here is my working:

$$\frac{dy}{dx} = \frac{-x}{2y}$$

$\int2ydy = \int-xdx$

$\frac{2y^2}{2} = \frac{-x^2}{2} + C$

Multiply both sides by 2:

$2y^2 = -x^2 + 2C$

What do I do next in order to solve the equation for the original equation?
• Feb 21st 2011, 11:20 AM
Ackbeet
Well, you're pretty much done, aren't you? The only thing you could do is absorb the 2 into the C. If you want to solve for y, you could, I suppose. Make sure that when you take your square root, and you get two roots, that the ones you present as your solution actually satisfy the original DE.
• Feb 21st 2011, 01:05 PM
sparky
Hi Ackbeet,

$X^2 + 2Y^2 = 0$

My question is, what happened to the C (or 2C)?

If I bring everything except the C over, I get $2Y^2 + X^2 = 2C$. How did he get 0?
• Feb 21st 2011, 01:17 PM
Ackbeet
There's only one way to get C=0: you have an initial condition (which would have to be y(0)=0). Otherwise, you must have the C there.
• Feb 21st 2011, 01:22 PM
sparky
Ok thanks Ackbeet!
• Feb 21st 2011, 01:24 PM
Ackbeet
You're welcome. Have a good one!