What is a solution to the differential equation #dy/dx=(3y)/(2+x)#?

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Answer 1 · 2016-07-19T20:02:57

#y = e^(3C)(2+x)^(3)#

# = C(2+x)^(3)#

This differential equation is separable.

#dy/(dx) = (3y)/(2+x)#

#dy = (3y)/(2+x) dx#

#1/(3y) dy = 1/(2+x) dx#

#int 1/(3y) dy = int 1/(2+x) dx#

#1/3 int 1/y dy = int 1/(2+x) dx#

#1/3 ln y = ln(2+x) + C#

#ln y = 3[ln(2+x)+C]#

#y = e^(3[ln(2+x)+C])#

#y = e^(3C)(2+x)^(3)#

#y = color(red)(C)(2+x)^(3)#

[where C is generic constant]