Choose the correct answer from the given four option. Integrating… - Vidyadip

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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