The differential equation of y=ae^{bx} (where | vedclass

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(B) Given equation: $y = ae^{bx} \dots (i)$ Differentiating with respect to $x$: $y_1 = \frac{dy}{dx} = abe^{bx}$ Since $y = ae^{bx}$, we can write: $

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$yy_2=y_1^2$

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(B) Given equation: $y = ae^{bx} \dots (i)$ Differentiating with respect to $x$: $y_1 = \frac{dy}{dx} = abe^{bx}$ Since $y = ae^{bx}$, we can write: $y_1 = by \dots (ii)$ Differentiating $y_1 = by$ with respect to $x$: $y_2 = \frac{d^2y}{dx^2} = by_1 \dots (iii)$ From equation $(ii)$, we have $b = \frac{y_1}{y}$. Substituting $b$ into equation $(iii)$: $y_2 = \left(\frac{y_1}{y}\right)y_1$ $y_2 = \frac{y_1^2}{y}$ Therefore, $yy_2 = y_1^2$.

The differential equation of $y=ae^{bx}$ (where $a$ and $b$ are parameters) is:

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