Question

Let $y=f(x)$ satisfies the differential equation $xy(1+y)dx=dy$. If $f(0)=1$ and $f(2)=\frac{e^2}{k-e^2}$ then $k$ is equal to

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (B)

$\frac{dy}{dx}=xy(1+y)\Rightarrow \int \frac{dy}{y(1+y)}=\int xdx\Rightarrow \frac{2y}{1+y}=e^{\frac{x^2}{2}}[$ As $f(0)=1]$
$\therefore f(2)=\frac{e^2}{2-e^2}$