ExamBro
ExamBro
TS EAMCET · Maths · Differential Equations

The solution of \(\left(1+x^2\right) \frac{d y}{d x}+2 x y-4 x^2=0\) is :

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

Answer & Solution

Correct Answer

(B) \(3 y\left(1+x^2\right)=4 x^3+c\)

Step-by-step Solution

Detailed explanation

\(\left(1+x^2\right) \frac{d y}{d x}+2 x y-4 x^2=0\) \(\Rightarrow \quad \frac{d y}{d x}+\left(\frac{2 x}{1+x^2}\right) y=\frac{4 x^2}{1+x^2}\) On comparing with \(\frac{d y}{d x}+P y=Q\), we get \(P=\frac{2 x}{1+x^2}, Q=\frac{4 x^2}{1+x^2}\) I.F.…