How do you find the general solution to #dy/dx=(2x)/e^(2y)#?

Question

10588 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-24T17:38:05

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

#dy/dx=(2x)/e^(2y)#

this is separable

#e^(2y)dy/dx=2x#

#int \ e^(2y)dy/dx \ dx=int \ 2x \ dx#

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

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

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

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