Question

Solve the differential equation: $(x+2y^3)\frac{dy}{dx}=y$

• A. $x=2y(y^2+c)$
• B. $x=y(y^2+c)$
• C. $x=y(2y^2+c)$
• D. None of these

Answer 1

Answer: (B)

$x=y(y^2+c)$

the given differential equation can be written as $\frac{dx}{dy}-\frac{x}{y}=2y^2$

It is in the form of linear equation

The integration factor of linear equation is $e^{\int -\frac{1}{y}dy}=\frac{1}{y}$

The general solution is $x\times \frac{1}{y}=\int 2y^2\times \frac{1}{y}dy+c=y^2+c$

therefore the general solution is $x=y(y^2+c)$

The correct option is $B$