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

MCQ

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

A
$y_2-3 y_1+3 y=0$
B
$x y_2+3 y_1-x y+x^2+3=0$
✓
$y_2-9 y=0$
D
$\left(y_1\right)^3-3 y\left(x y_2-3 y\right)=0$

✓

Answer

Correct option: C.

$y_2-9 y=0$

(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 w.r.t. $x$, we get
$
\begin{array}{l}
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
\end{array}
$

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