TS EAMCET · Maths · Differential Equations
The solution of the differential equation \(x y^2 d y-\left(x^3+y^3\right) d x=0\) is
- A \(y^3=3 x^3+c\)
- B \(y^3=3 x^3 \log (c x)\)
- C \(y^3=3 x^3+\log (c x)\)
- D \(y^3+3 x^3=\log (c x)\)
Answer & Solution
Correct Answer
(B) \(y^3=3 x^3 \log (c x)\)
Step-by-step Solution
Detailed explanation
Given differential equation can be rewritten as \[ \frac{d y}{d x}=\frac{x^3+y^3}{x y^2} \] It is a homogeneous differential equation. Put \[ y=v x \Rightarrow \frac{d y}{d x}=v+x \frac{d v}{d x} \]…
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