Question

The general solution of the differential equation $\left(2x\ln y\right)dx+(\frac{x^2}{y}+3y^2)dy=0$ is
(where $c$ is constant of integration)

• A. $x\ln y+y^2=c$
• B. $2x^2\ln y+y^3=c$
• C. $x^2\ln y+y^3=c$
• D. $x^2\ln y+y^2=c$

Answer 1

The correct option is C $x^2\ln y+y^3=c$

$\left(2x\ln y\right)dx+(\frac{x^2}{y}+3y^2)dy=0$
$\Rightarrow \left(2x\ln y\right)dx+\frac{x^2}{y}dy+3y^{2}dy=0$
$\Rightarrow d\left(x^2\ln y\right)+d\left(y^3\right)=0$
Integrating both sides, we get
$x^2\ln y+y^3=c$