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TS EAMCET · Maths · Differential Equations

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

  1. A \(x=y^3+c\)
  2. B \(x=y^3+c y\)
  3. C \(y=x^3+c\)
  4. D \(y=x^3+c x+d\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(y=x^3+c x+d\)

Step-by-step Solution

Detailed explanation

We have, \(\left(x+2 y^3\right) \frac{d y}{d x}=y\) \(\begin{aligned} \Rightarrow & y \frac{d x}{d y} & =x+2 y^3 \\ \Rightarrow & \frac{d x}{d y}-\frac{x}{y} & =2 y^2\end{aligned}\) It is linear differential equation of the firm \(\frac{d x}{d y}+P x=Q\)…