Example1.求解下列微分方程(1)y+2y-3y=0, (2)y"-2y+y=0,(3)y+4y+5y=0, (4)y"-4y3=0,(5)y"+y=0 Solution.(1)特征方程为r2+2r-3=0, 解得n=1,n2=-3 故所求通解为p=Ce+C2e-3x (2)特征方程为r2-2r+1=0, 解得 故所求通解为y=(C1+C2x)e KExample 1. 求解下列微分方程 (1) y + 2 y − 3 y = 0, (2) y − 2 y + y = 0, (3) y + 4 y + 5 y = 0, (4) y − 4 y = 0, (5) y + y = 0. Solution. (1)特征方程为 2 3 0, 2 r + r − = 解得 r1 = 1,r2 = −3 故所求通解为 . 3 1 2 x x y C e C e − = + (2)特征方程为 2 1 0, 2 r − r + = 解得 r1 = r2 = 1 故所求通解为 ( ) . 1 2 x y = C + C x e