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TS EAMCET · Maths · Differential Equations

The general solution of the differential equation \(\left(2 x-10 y^3\right) d y+y d x=0, y \neq 0\) is

  1. A \(x^2 y-2 y^3=c\)
  2. B \(x y^2-2 y^5=c\)
  3. C \(x y^3+2 y=c\)
  4. D \(x y^2+3 y=c\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(x y^2-2 y^5=c\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \left(2 x-10 y^3\right) d y+y d x=0 \\ \Rightarrow & y d x=\left(10 y^3-2 x\right) d y \\ \Rightarrow & \frac{d x}{d y}=10 y^2-2 \frac{x}{y} \Rightarrow \frac{d x}{d y}+2 \frac{x}{y}=10 y^2 \\ \Rightarrow & \frac{d x}{d y}+P x=Q \Rightarrow I F=e^{\int…