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Differential Equations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDifferential Equations1 Mark
MCQ
The solution of differential equation $\frac{\text{dy}}{\text{dx}}-3\text{y}=\sin2\text{x}$ is:
  • A
    $\text{y}=\text{e}^{-3\text{x}}\Big[\frac{\cos2\text{x}+3\sin2\text{x}}{13}\Big]+\text{c}$
  • B
    $\text{y}=\text{e}^{-3\text{x}}\Big[\frac{\cos2\text{x}-3\sin2\text{x}}{13}\Big]+\text{c}$
  • ✓
    $\text{y}^{-3\text{x}}=-\text{e}^{-3\text{x}}\Big[\frac{2\cos2\text{x}+3\sin2\text{x}}{13}\Big]+\text{c}$
  • D
    None of these
✓

Answer

Correct option: C.
$\text{y}^{-3\text{x}}=-\text{e}^{-3\text{x}}\Big[\frac{2\cos2\text{x}+3\sin2\text{x}}{13}\Big]+\text{c}$

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