Verify that the function y = e-3x is a solution of the differenti… - Vidyadip

Question

Verify that the function y = e^-3x is a solution of the differential equation $\frac{d^{2} y}{d x^{2}}+\frac{d y}{d x}$ - 6y = 0

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Answer

Given function is y = e^-3x
Differentiating both sides of equation with respect to x , we get
$\frac{d y}{d x}=-3 e^{-3x}$ ...(i)
Now, differentiating (1) with respect to x, we have$\frac{d^{2} y}{d x^{2}}=9 e^{-3 x}$
Substituting the values of $\frac{d^{2} y}{d x^{2}}, \frac{d y}{d x}$ and y in the given differential equation, we get
L.H.S. = 9.e^-3x + (-3.e^-3x) - 6.e^-3x = 9.e^-3x - 9.e^-3x = 0 = R.H.S.
Therefore, the given function is a solution of the given differential equation.

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