TS EAMCET · Maths · Differential Equations
The general solution of the differential equation \(x^2 y d x-\left(x^3+y^3\right) d y=0\) is
- A \(y^3=3 x^3 \log (c x)\)
- B \(c\left(x^3-y^3\right)=x^2\)
- C \(\log |y|-\frac{x^3}{3 y^3}=c\)
- D \(y^2-x^2=c^2\left(y^2-x^2\right)\)
Answer & Solution
Correct Answer
(C) \(\log |y|-\frac{x^3}{3 y^3}=c\)
Step-by-step Solution
Detailed explanation
We have, \[ x^2 y d x-\left(x^3+y^3\right) d y=0 \Rightarrow \frac{d y}{d x}=\frac{x^2 y}{x^3+y^3} \] Given differentiate equation is in the form of homogeneous differentiate equation. So, let \(y=v x\)…
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