Question

2y'+3y=e2x

Answer 1

Solution :

$y'(x) = \frac{e^{2x}}{2} - \frac{3 y(x)}{2}\\$

Find the integration factor $\mu=e^\frac{3x}{2}$

Put the equation in the form ($(\mu(x)*y)'=\mu(x)q(x):\,(e^\frac{3x}{2}y)'= \frac{e^{\frac{7x}{2}}}{2}$

Solve: $(e^{\frac{3x}{2}}y)'= \frac{e^{\frac{7x}{2}}}{2}$

$y(x) = \frac{c_1}{e^\frac{3x}{2}} + \frac{e^{2 x}}{7}$