Question

The solution of the given differential equation $\frac{dy}{dx}+2xy=y$ is

• A. $y=c{e}^{x-x^2}$
  
• B. $y=c{e}^{x^2-x}$
  
• C. $y=c{e}^x$
  
• D. $y=c{e}^{-x^2}$

Answer 1

The correct option is A $y=c{e}^{x-x^2}$


$\frac{dy}{dx}+(2x-1)y=0$; I.F.=$e^{\int (2x-1)dx}=e^{x^2-x}$
Required solution is $y{e}^{x^2-x}=c$ or $y=c{e}^{x-x^2}$