Question

Find a general solution to the differential equation 2y''-5y'-3y=0

Answer 1

We want a general solution for the ODE
2y'' - 5y' - 3y = 0

The characteristic equation is
2m² - 5m - 3 = 0
(2m + 1)(m - 3) = 0
which yields
m = -1/2, 3

Answer:
The general solution is

`y(x)=c_(1)e^(-x/2)+c_(2) e^(3x)`
where c₁ and c₂ are constants.