Question

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

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

Answer 1

Answer: (D)

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