If $2 x^{2} + 11 x y + 3 y^{2} = 0$ where p,q,r are constants then prove that $\frac{d^{2} y}{d x^{2}} = 0$

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Solution

$\begin{matrix} 2 x^{2} + 11 x y + 3 y^{2} = 0 4 x + 11 x \frac{d y}{d x} + 11 y + 6 y \frac{d y}{d x} = 0 d i f f e r e n t i a t e a g a i n 4 + 11 x \frac{d^{2} y}{d x^{2}} + 11 \frac{d y}{d x} + 11 \frac{d y}{d x} + 6 {(\frac{d y}{d x})}^{2} + 6 y \frac{d^{2} y}{d x^{2}} = 0 \end{matrix}$

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