📚 How to find the particular solution of a second-order differential equation

Solve y^′′−4y^′+3y=0 if y^′=5 at (1, 2).

What you'll need:

Form of second-order DE, right side zero: (ay^′′+by^′+cy=0)

Auxiliary equations of second-order DE, right side zero: (am^2+bm+c=0)

General solution of second-order DE, right side zero: (y=c_1 e^(m_1 x)+c_2 e^(m_2 x) )