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

1 Answer
Jul 19, 2016

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

= C(2+x)^(3)

Explanation:

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]