TS EAMCET · Maths · Differential Equations
The general solution of the differential equation \(\left(3 x^2-2 x y\right)\) \(d y+\left(y^2-2 x y\right) d x=0\) is
- A \(x^2-x y=c y^2\)
- B \(y^2-x y=c x^3\)
- C \(x y-x^2=c y^3\)
- D \(x y-y^2=c y^3\)
Answer & Solution
Correct Answer
(C) \(x y-x^2=c y^3\)
Step-by-step Solution
Detailed explanation
\begin{aligned} \begin{aligned} & \left(3 x^2-2 x y\right) d y+\left(y^2-2 x y\right) d x=0 \\ \Rightarrow & \frac{d y}{d x}=\frac{2 x y-y^2}{3 x^2-2 x y} \\ \Rightarrow & P u t y=v x \Rightarrow \frac{d y}{d x}=v+x \frac{d v}{d x} \\ \Rightarrow & v+x \frac{d v}{d x}=\frac{2…
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