Question

The solution of the differential equation $\frac{d x}{d y}+2 y x=2 y$ which passes through the point $(2,0)$ is

• A. $(x-1)=2 e^{y^{2}}$
• B. $(x-1)=2 e^{-y^{2}}$
• C. $(x-1)=e^{y^{2}}$
• D. $(x-1)=e^{-y^{2}}$

Answer 1

Answer: (D)

Given differential equation is,
$\frac{d x}{d y}+2 y \cdot x=2 y$
$\Rightarrow \frac{d x}{d y}=2 y(1-x)$
$\Rightarrow \int \frac{d x}{1-x}=\int 2 y d y$
$\Rightarrow -\log (x-1)=y^{2}+c$
Since, curve (i) passes through the point $(2,0)$, so $c=0$
So, curve will be $(x-1)=e^{-y^{2}}$