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AP EAMCET · Maths · Differential Equations

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

  1. A \(c x y^2=e^{\frac{x}{y}}\)
  2. B \(c x y^2 e^{\frac{x}{y}}=1\)
  3. C \(c x y e^{\frac{x}{y}}=1\)
  4. D \(c x y=e^{\frac{x}{y}}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(c x y^2 e^{\frac{x}{y}}=1\)

Step-by-step Solution

Detailed explanation

\(\begin{array}{r} \left(x y+y^2\right) d x-\left(x^2-2 x y\right) d y=0 \\ \frac{d y}{d x}=\frac{\left(x y+y^2\right)}{\left(x^2-2 x y\right)} \Rightarrow \frac{d y}{d x}=\frac{\frac{y}{x}+\left(\frac{y}{x}\right)^2}{1-2\left(\frac{y}{x}\right)} \end{array}\) Let…