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9. differential equations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths9. differential equations1 Mark
MCQ
The solution of the differential equation $\frac{{dy}}{{dx}} = (a{e^{bx}} + c\cos mx)$ is
  • A
    $y = \frac{{a{e^x}}}{b} + \frac{c}{m}\sin mx + k$
  • B
    $y = a{e^x} + c\sin mx + k$
  • ✓
    $y = \frac{{a{e^{bx}}}}{b} + \frac{c}{m}\sin mx + k$
  • D
    None of these
✓

Answer

Correct option: C.
$y = \frac{{a{e^{bx}}}}{b} + \frac{c}{m}\sin mx + k$
c
(c) $\frac{{dy}}{{dx}} = (a{e^{bx}} + c\cos mx)$ ==> $dy = (a{e^{bx}} + c\cos mx)dx$

On integrating, $y = \frac{{a{e^{bx}}}}{b} + \frac{{c\sin (mx)}}{m} + k$.

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