JEE Mains · Maths · STD 12 - 9. differential equations
The solution of the differential equation \(\left(x^2+y^2\right) d x-5 x y d y=0, y(1)=0\), is :
- A \(\left|x^2-4 y^2\right|^5=x^2\)
- B \(\left|\mathrm{x}^2-2 \mathrm{y}^2\right|^6=\mathrm{x}\)
- C \(\left|x^2-4 y^2\right|^6=x\)
- D \(\left|x^2-2 y^2\right|^5=x^2\)
Answer & Solution
Correct Answer
(A) \(\left|x^2-4 y^2\right|^5=x^2\)
Step-by-step Solution
Detailed explanation
\( \left(x^2+y^2\right) d x=5 x y d y \) \( \Rightarrow \frac{d y}{d x}=\frac{x^2+y^2}{5 x y}\) Put \(y=V x\) \( \Rightarrow \mathrm{V}+\mathrm{x} \frac{\mathrm{dv}}{\mathrm{dx}}=\frac{1+\mathrm{V}^2}{5 \mathrm{~V}} \)…
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