JEE Mains · Maths · STD 12 - 9. differential equations
If \(y \frac{d y}{d x}=x\left[\frac{y^{2}}{x^{2}}+\frac{\phi\left(\frac{y^{2}}{x^{2}}\right)}{\phi^{\prime}\left(\frac{y^{2}}{x^{2}}\right)}\right], x>0, \phi>0\), and \(y(1)=-1\) then \(\phi\left(\frac{\mathrm{y}^{2}}{4}\right)\) is equal to :
- A \(4 \,\phi(2)\)
- B \(4\, \phi(1)\)
- C \(2 \,\phi(1)\)
- D \(\phi\) \((1)\)
Answer & Solution
Correct Answer
(B) \(4\, \phi(1)\)
Step-by-step Solution
Detailed explanation
Let, \(y=t x\) \(\frac{d y}{d x}=t+x \frac{d t}{d x}\) \(\therefore t x\left(t+x \frac{d t}{d x}\right)=x\left(t^{2}+\frac{\varphi\left(t^{2}\right)}{\varphi^{\prime}\left(t^{2}\right)}\right)\)…
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