If $y\frac{\text{dy}}{\text{dx}} = x\left\lbrack \frac{y^{2}}{x^{2}} + \frac{\phi\left( \frac{y^{2}}{x^{2}} \right)}{\phi'\left( \frac{y^{2}}{x^{2}} \right)},x 0,\phi 0 \right\rbrack$ and $y(1) = - 1$, then $\phi\left( \frac{y^{2}}{4} \right)$ is equal to: [JEE Main 2021, 31 Aug (Shift 2)]

Question

If $y\frac{\text{dy}}{\text{dx}} = x\left\lbrack \frac{y^{2}}{x^{2}} + \frac{\phi\left( \frac{y^{2}}{x^{2}} \right)}{\phi'\left( \frac{y^{2}}{x^{2}} \right)},x > 0,\phi > 0 \right\rbrack$ and $y(1) = - 1$, then $\phi\left( \frac{y^{2}}{4} \right)$ is equal to: [JEE Main 2021, 31 Aug (Shift 2)]

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If \(y\frac{\text{dy}}{\text{dx}} = x\left\lbrack \frac{y^{2}}{x^{2}} + \frac{\phi\left( \frac{y^{2}}{x^{2}} \right)}{\p…

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