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Differential Equations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDifferential Equations1 Mark
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.
$y_2-9 y=0$
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
$y_2=9 A e^{3 x}+9 B e^{-3 x}$
$=9\left(A e^{3 x}+B e^{-3 x}\right)$
$=9 y$
$\Rightarrow y_2-9 y$
$=0$

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