Question

If $y(x)$ is solution of $(x+1)\frac{dy}{dx}-xy=1,y(0)=-1$, then $y\left(\frac{-6}{5}\right)$ is equal to

• A. 7
• B. 5
• C. 3
• D. 1

Answer 1

Answer: (B)

We have $\frac{dy}{dx}-\frac{x}{x+1}\cdot y=\frac{1}{x+1}$ (linear differential equation) So, general solution is
$y(x+1)e^{-x}=\int e^{-x}dx+C\Rightarrow y(x+1)e^{-x}=-e^{-x}+C$
As $y(0)=-1$, gives $C=0$
$\Rightarrow y(x+1)=-1\Rightarrow y=\frac{-1}{1+x}$
$\therefore y\left(\frac{-6}{5}\right)=5$