What is a solution to the differential equation #(2+x)y'=2y#?

Question

1622 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-07T21:37:49

# y = beta (2+x)^2#

this is separable

#(2+x)y'=2y#

#1/y y'=2/(2+x) #

#int \ 1/y \ dy=int \ 2/(2+x) \ dx #

#ln y = 2 ln (2+x) + alpha#

#ln y = 2 ln (2+x) + ln beta#

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

# y = beta (2+x)^2#