Q120 / 160 · AP EAMCET 2024 (21 May Shift 1) · Mathematics

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

  • A
    $x=y(2 x y+c)$
  • Correct answer
    B
    $x=y\left(y^2+c\right)$
  • C
    $y=x\left(x^2+c\right)$
  • D
    $x y=\frac{y^4}{2}+c$

Solution

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

Hence, the correct answer is option: 'B'.

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