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
- A \(c x y^2=e^{\frac{x}{y}}\)
- B \(c x y^2 e^{\frac{x}{y}}=1\)
- C \(c x y e^{\frac{x}{y}}=1\)
- D \(c x y=e^{\frac{x}{y}}\)
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…
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