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TS EAMCET · Maths · Differential Equations

The solution of \(\left(y-3 x^2\right) d x+x d y=0\) is

  1. A \(y(x)=\sin x+\frac{1}{x^2}+C\)
  2. B \(y(x)=\cos x-\frac{1}{x^2}+C\)
  3. C \(y(x)=x^2+\frac{C}{x}\)
  4. D \(y(x)=\sqrt{x}+\frac{C}{x}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(y(x)=x^2+\frac{C}{x}\)

Step-by-step Solution

Detailed explanation

We have, \[ \begin{array}{rlrl} & & \left(y-3 x^2\right) d x+x d y & =0 \\ \Rightarrow & y d x-3 x^2 d x+x d y & =0 \\ \Rightarrow & & y d x+x d y & =3 x^2 d x \\ \Rightarrow & & d x y & =3 x^2 d x \end{array} \] On integrating both sides, we get…