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AP EAMCET · Maths · Differential Equations

The solution of differential equation \(\left(x+2 y^3\right) \frac{d y}{d x}=y\) is

  1. A \(x=y(2 x y+c)\)
  2. B \(x=y\left(y^2+c\right)\)
  3. C \(y=x\left(x^2+c\right)\)
  4. D \(x y=\frac{y^4}{2}+c\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(x=y\left(y^2+c\right)\)

Step-by-step Solution

Detailed explanation

\(\begin{aligned} & \text { }\left(x+2 y^3\right) \frac{d y}{d x}=y \Rightarrow \frac{d x}{d y}=\frac{x+2 y^3}{y} \\ & \Rightarrow \frac{d x}{d y}-\frac{x}{y}=2 y^2 ; \text { I.F. }=e^{\int \frac{-1}{y} d y}=\frac{1}{y} \end{aligned}\) Solution:…