Question

For the given differential equation, find the general solution: $(x+3y^2) \frac{dy}{dx}=y(y\ \textgreater \ 0)$

Answer 1

Answer:

The required solution is $3y=\frac{x}{y}+c$

Step-by-step explanation:

concept:

I have applied varible separable method to solve this differential equation.

$(x+3y^2)\frac{dy}{dx}=y\\\\(x+3y^2)dy=y\:dx\\\\x\:dy+3y^2dy=y\:dx\\\\3y^2dy=y\:dx-x\:dy\\\\3\:dy=\frac{y\:dx-x\:dy}{y^2}\\\\3\:dy=d(\frac{x}{y})$

Integrating on both sides we get

$3\int{dy}=\int{d(\frac{x}{y})}\\\\3y=\frac{x}{y}+c$