Question

The solution of the differential equation $\frac{dy}{dx}+\frac{3x^2}{1+x^3}y=\frac{si{n}^{2}x}{1+x^3}$ is

• A.
  
• B.
  
• C.
  
• D.
  

Answer 1

The correct option is D

$\frac{dy}{dx}+\frac{3x^2}{1+x^3}y=\frac{si{n}^{2}x}{1+x^3}P=\frac{3x^2}{1+x^3}\Rightarrow I.F.=e^{\int pdx}=e^{log(1+x^3)=1+x^3}$
Thus the solution is
$y.(1+x^3)=\int \frac{si{n}^{2}x}{1+x^3}(1+x^3)dx=\int \frac{1-cos2x}{2}dx\Rightarrow y(1+x^3)=\frac{1}{2}x-\frac{sin2x}{4}+c.$