JEE Mains · Maths · STD 12 - 9. differential equations
Let the solution curve of the differential equation \(xdy-ydx=\sqrt{x^{2}+y^{2}}dx, x>0, y(1)=0\), be \(y=y(x)\). Then \(y(3)\) is equal to
- A 4
- B 6
- C 1
- D 2
Answer & Solution
Correct Answer
(A) 4
Step-by-step Solution
Detailed explanation
\(\frac{x d y-y d x}{x^2}=\frac{\sqrt{x^2+y^2}}{x^2} d x\) \(d \left(\frac{ y }{ x }\right)=\sqrt{1+\frac{ y ^2}{ x ^2}} \cdot \frac{1}{ x } dx\) \(\int \frac{ d \left(\frac{ y }{ x }\right)}{\sqrt{1+\left(\frac{ y }{ x }\right)^2}}=\int \frac{1}{ x } dx\)…
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