Solve the following differential equation dy dx =e^ x+y +x^2e^y - Vidyadip

Question

Solve the following differential equation
$\frac{\text{dy}}{\text{dx}}=\text{e}^{\text{x}+\text{y}}+\text{x}^2\text{e}^\text{y}$

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Answer

$\frac{\text{dy}}{\text{dx}}=\text{e}^{\text{x}+\text{y}}+\text{x}^2\text{e}^\text{y}$
$=\text{e}^\text{x}\text{e}^\text{y}+\text{x}^2\text{e}^\text{y}$
$\frac{\text{dy}}{\text{dx}}=\text{e}^\text{y}(\text{e}^\text{x}+\text{x}^2)$
$\int\text{e}^{-\text{y}}\text{dy}=\int(\text{e}^\text{x}+\text{x}^2)\text{dx}$
$-\text{e}^{_\text{y}}=\text{e}^\text{x}+\frac{\text{x}^3}{3}+\text{C}$

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