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
- A \(x^2 y-2 y^3=c\)
- B \(x y^2-2 y^5=c\)
- C \(x y^3+2 y=c\)
- D \(x y^2+3 y=c\)
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…
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