Solve the following differential equation (x+2) dy dx =x^2+3x+7 - Vidyadip

Question

Solve the following differential equation
$(\text{x}+2)\frac{\text{dy}}{\text{dx}}=\text{x}^2+3\text{x}+7$

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Answer

$(\text{x}+2)\frac{\text{dy}}{\text{dx}}=\text{x}^2+3\text{x}+7$
$\text{dy}=\Big(\frac{\text{x}^2+3\text{x}+7}{\text{x}+2}\Big)\text{dx}$
$\text{dy}-\Big(\text{x}+1+\frac{5}{\text{x}+2}\Big)\text{dx}$
$\int\text{dy}-\int\Big(\text{x}+1+\frac{5}{\text{x}+2}\Big)\text{dx}$
$\text{y}=\frac{\text{x}^2}{2}+\text{x}+5\log|\text{x}+2|+\text{C}$
$\text{x}\neq-2$

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