The differential equation whose solution is y=A e^ 3 x +B e^ -3 x… - Vidyadip

Question

The differential equation whose solution is $y=A e^{3 x}+B e^{-3 x}$ is given by

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Answer

$(c) :$ We have, $y=A e^{3 x}+B e^{-3 x}$
Differentiating w.r.t. $x$, we get
$y_1=3 A e^{3 x}-3 B e^{-3 x}$
Again differentiating $\text{w.r.t. x}$, we get
$y_2=9 A e^{3 x}+9 B e^{-3 x}=9\left(A e^{3 x}+B e^{-3 x}\right)=9 y$
$\Rightarrow y_2-9 y=0$

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