# What is a solution to the differential equation #dy/dx=(2x)/e^(2y)#?

##### 1 Answer

Dec 14, 2016

#y = lnsqrt(2x^2)#

#### Explanation:

This is a separable differential equation.

#dy(e^(2y)) = 2xdx#

#int(dye^(2y)) = int(2xdx)#

#1/2e^(2y) = x^2#

It is often preferable to solve for

#e^(2y) = x^2/(1/2)#

#e^(2y) = 2x^2#

#ln(e^(2y)) = ln(2x^2)#

#2ylne = ln(2x^2)#

#2y = ln(2x^2)#

#y = 1/2ln(2x^2)#

#y = lnsqrt(2x^2)#

Hopefully this helps!