AP EAMCET · Maths · Differential Equations
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 & Solution
Correct Answer
(D) \((x-1)=e^{-y^2}\)
Step-by-step Solution
Detailed explanation
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…
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