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The D.E of the family of curves given by $y = a e^{2 x} + b e^{5 x}$ where a,b are parameters is

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$\frac{d^{2} y}{d x^{2}} + 7 \frac{d y}{d x} - 10 y = 0$

$\frac{d^{2} y}{d x^{2}} - 7 \frac{d y}{d x} - 10 y = 0$

$\frac{d^{2} y}{d x^{2}} - 7 \frac{d y}{d x} + 10 y = 0$

$\frac{d^{2} y}{d x^{2}} + 7 \frac{d y}{d x} + 10 y = 0$

answer is C.

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Detailed Solution

$\frac{d^{2} y}{d x^{2}} - (α_{1} + α_{2}) \frac{d y}{d x} + α_{1} α_{2} y = 0$
Where $α_{1} = 2, α_{2} = 5$

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