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DIFFERENTIAL EQUATIONS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDIFFERENTIAL EQUATIONS1 Mark
MCQ
Choose the correct answer from the given four option.
Integrating factor of $\frac{\text{xd}\text{y}}{\text{d}\text{x}}-\text{y}=\text{x}^4-3\text{x}$ is:
  • A
    $\text{x}$
  • B
    $\log\text{x}$
  • ✓
    $\frac{1}{\text{x}}$
  • D
    $-\text{x}$
✓

Answer

Correct option: C.
$\frac{1}{\text{x}}$
Given that $\frac{\text{xd}\text{y}}{\text{d}\text{x}}-\text{y}=\text{x}^4-3\text{x}$

Dividing both sides by x, we get

$\Rightarrow\frac{\text{d}\text{y}}{\text{d}\text{x}}-\frac{\text{y}}{\text{x}}=\text{x}^3-3$

Here, $\text{P}=-\frac{1}{\text{x}},\text{Q}=\text{x}^3-3$

$\therefore\text{I.F.}=\text{e}^{\int\text{Pdx}}=\text{e}^{-\int\frac{1}{\text{x}}\text{dx}}$

$\text{e}^{-\log\text{x}}=\frac{1}{\text{x}}$

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