What is a solution to the differential equation \frac{dy}{dx}=\frac{3y}{2+x}?

Hallie Watts

Hallie Watts

Answered question

2022-04-18

What is a solution to the differential equation dydx=3y2+x?

Answer & Explanation

rhyclelal80j6

rhyclelal80j6

Beginner2022-04-19Added 13 answers

This differential equation is separable.
dydx=3y2+x
dy=3y2+xdx
13ydy=12+xdx
13ydy=12+xdx
131ydy=12+xdx
13lny=ln(2+x)+C
lny=3[ln(2+x)+C]
y=e3[ln(2+x)+C]
y=e3C(2+x)3
y=C(2+x)3
[where C is generic constant]

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