Question

The solution of the equation $(x+2y^3)\frac{dy}{dx}-y=0$ is

[MP PET 1998; 2002]

• A.
  
• B.
• C.
• D.
  

Answer 1

The correct option is B

$(x+2y^3)\frac{dy}{dx}=y\Rightarrow \frac{dy}{dx}=\frac{y}{x+2y^3}$
$\Rightarrow \frac{dx}{dy}=\frac{x+2y^3}{y}or\frac{dx}{dy}-\frac{x}{y}=2y^2,$ which is a linear equation of the form $\frac{dx}{dy}+Px=Q$
So, integrating factor $(I.F.)=e^{-\int \frac{1}{y}dy}$
and solution is $x\frac{1}{y}=\int \frac{1}{y}2y^{2}dy+A=y^2+A\Rightarrow x=y^3+Ay$
$\Rightarrow y^3-x=Ay;$ Where A can be -ve or +ve.