The general solution of the differential equation y'' + 3y' + 2y = 0 is confirmed as y = c_1e^-2x + c_2e^-x. The characteristic equation r^2 + 3r + 2 = 0 is solved by factoring into (r+2)(r+1), yielding roots r = -2 and r = -1. This solution is validated by substituting back into the original equation, confirming its correctness.
PREREQUISITESStudents studying differential equations, educators teaching mathematical methods, and anyone seeking to understand the solutions of linear differential equations.
This is easy enough to check. For you solution, it should be that y'' + 3y' + 2y = 0. If so, your solution is correct.darryw said:Homework Statement
"find the general solution of the equation: y'' + 3y' + 2y = 0
characteristic is:
r^2 + 3r + 2 = 0
solve quadratic:
(r+2)(r+1)
r = -2
r= -1
therefore GS of equation is: y = c_1e^-2x + c_2e^-x
thanks for any help