Find the general solution of (x+3)y’=2y

Question

asked Sep 23, 2022 34.3k views

1 Answer

Rizky Ramadhan · Answer 1 · 2022-09-30T11:35:21+0000

Answer:

y=C(x+3)^2

Explanation:

We are given:

$\displaystyle (x+3)y^\prime=2y$

Separation of Variables:

$\displaystyle (1)/(y)(dy)/(dx)=(2)/(x+3)$

So:

$\displaystyle (dy)/(y)=(2)/(x+3) \, dx$

Integrate:

$\displaystyle \int(dy)/(y)=\int(2)/(x+3)\, dx$

Integrate:

$\displaystyle \ln|y|=2\ln|x+3|+C$

Raise both sides to e:

$|y|=e^(2\ln|x+3|+C)$

Simplify:

$|y|=(e^(\ln|x+3|))^2\cdot e^C$

So:

|y|=C|x+3|^2

Simplify:

$y=\pm C(x+3)^2=C(x+3)^2$