Differential equations course

Question

A second order homogeneous lines differential equation with constant us given as follows

2y"(t)+3y'(t)-2y(t)=0

A. Find the general solution of the equation.

B. Suppose that the solution y(t) has a local extreme value at y=1 . Then determine the value of the second order derivative y" at this extreme value point and state the extreme value is maximum it minimal

Answer 1

(2D² + 3D - 2) y(t) = 0

(2D - 1)(D + 2) y(t) = 0

y(t) = C₁e^t/2 + C₂e^-2t is the general solution.