Self Quiz Solutions 32 - Introduction to Differential Equations | MATH 220, Study notes of Differential Equations

Download Self Quiz Solutions 32 - Introduction to Differential Equations | MATH 220 and more Study notes Differential Equations in PDF only on Docsity! MATH 220 Self-quiz 32 1. Solve the initial value problem: y′′ − 3y′ + 2y′ = 0 y(0) = 2 y′(0) = 3 Solution: The auxiliary equation is: r2 − 3r + 2 = 0 that has rearl roots 1 and 2. This means that the general solution of the equation is: y = C1ex + C2e2x (1) To determine C1 and C2, we first find the derivative: y′ = C1ex + 2C2e2x (2) and we substitute 0 in (1) and (2) to get: C1 + C2 = 2 C2 + 2C2 = 3 This, easily, gives C1 = C2 = 1, which means that the solution of the initial value problem is: y = ex + e2x 2. Find the general solution of the differential equation: