Solve the following differential equation dy dx +2x=e^ 3x - Vidyadip

Question

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

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Answer

$\frac{\text{dy}}{\text{dx}}+2\text{x}=\text{e}^{3\text{x}}$
$\frac{\text{dy}}{\text{dx}}=\text{e}^{3\text{x}}-2\text{x}$
$\int\text{dy}=\int(\text{e}^{3\text{x}}-2\text{x})\text{dx}$
$\text{y}=\frac{\text{e}^{3\text{x}}}{3}-\frac{2\text{x}^2}{2}+\text{c}$
$\text{y}=\frac{\text{e}^{3\text{x}}}{3}-\text{x}^2+\text{c}$
$\text{y}+\text{x}^2=\frac{1}{3}\text{e}^{3\text{x}}+\text{c}$

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