JEE Mains · Maths · STD 12 - 9. differential equations
If \(y = y ( x )\) is the solution of the differential equation \(2 x^{2} \frac{d y}{d x}-2 x y+3 y^{2}=0 \quad\) such that \(y(e)=\frac{e}{3}\), then \(y(1)\) is equal to
- A 0.33
- B 0.67
- C 1.5
- D 3
Answer & Solution
Correct Answer
(B) 0.67
Step-by-step Solution
Detailed explanation
\(\frac{ dy }{ dx }-\frac{ y }{ x }=-\frac{3}{2}\left(\frac{ y }{ x }\right)^{2} \quad y = vx\) \(\frac{ dv }{ v ^{2}}=-\frac{3 dx }{2 x }\) \(-\frac{1}{ v }=-\frac{3}{2} \ln | x |+ C\) \(-\frac{ x }{ y }=\frac{-3}{2} \ln | x |+ C\) \(x = e , y =\frac{ e }{3}\)…
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