# 1sr order differential equation

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• March 28th 2009, 11:47 PM
zxcv
1sr order differential equation
Hi,

Can someone please help me by showing the step for how to do the following problem:

For what value k, is the 2xyy' + y^k = 0 an exaxt differential equation?
• March 29th 2009, 01:52 AM
mr fantastic
Quote:

Originally Posted by zxcv
Hi,

Can someone please help me by showing the step for how to do the following problem:

For what value k, is the 2xyy' + y^k = 0 an exaxt differential equation?

You have $2xy \, dy + y^k \, dx = 0$.

Read my reply here: http://www.mathhelpforum.com/math-he...ion-exact.html

You have $B = 2xy$ and $A = y^k$ and you require $\frac{\partial A}{\partial y} = \frac{\partial B}{\partial x}$.