Question
If sinx is an integrating factor of the differential equation $\frac{\text{dy}}{\text{dx}}+\text{Py}=\text{Q}$ than write the value of P.
✓
Answer
It is given that sinx is the intergrating factor of the differential equation $\frac{\text{dy}}{\text{dx}}+\text{Py}=\text{Q}.$
$\text{e}^{\int\text{P}\text{dy}}=\sin\text{x}$
$\Rightarrow \int \text{P}\ \text{dx}=\log|\sin\text{x}|$
$\Rightarrow \int \text{P}\ \text{dx}=\int\cot\text{x}\ \text{dx}$
$\Rightarrow \text{P}=\cot\text{x}$
$\text{e}^{\int\text{P}\text{dy}}=\sin\text{x}$
$\Rightarrow \int \text{P}\ \text{dx}=\log|\sin\text{x}|$
$\Rightarrow \int \text{P}\ \text{dx}=\int\cot\text{x}\ \text{dx}$
$\Rightarrow \text{P}=\cot\text{x}$
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