Q120 / 160 · AP EAMCET 2018 (23 Apr Shift 2) · Mathematics
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$(x-1)=e^{y^2}$
- Correct answerD$(x-1)=e^{-y^2}$
Solution
Given differential equation is,
$$
\begin{aligned}
& \quad \frac{d x}{d y}+2 y \cdot x=2 y \\
& \Rightarrow \frac{d x}{d y}=2 y(1-x) \Rightarrow \int \frac{d x}{1-x}=\int 2 y d y \\
& \Rightarrow \quad-\log (x-1)=y^2+c
\end{aligned}
$$
Since, curve (i) passes through the point $(2,0)$, so $c=0$
So, curve will be $(x-1)=e^{-y^2}$
Hence, the correct answer is option: 'D'.