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!
