Question

(a) find the general solution to y^{\,\prime\prime} + 3 y^{\,\prime} = 0. give your answer as y = . . . \ . in your answer, use c_1 and c_2 to denote arbitrary constants and x the independent variable. enter c_1 as c1 and c_2 as c2.

Answer 1

We want to solve
y'' + 3y' = 0

Solve the indicial equation.
m² + 3m = 0
m(m + 3) = 0
m = 0 or m = -3

The basic solutions are e⁰=1 and $e^{-3x}$.

Answer:
The general solution is
$y(x) = c_{1} + c_{2}e^{-3x}$