MAT 22B University of California Davis Differential Equation Questionnaire

Let ri, r2 be the roots (real and distinct) of the characteristic equation of the homogeneous
differential equation
ay” + by’ + cy= 0
Write yı(t) and y2(t) i.e. the fundamental solutions in terms of rı, r2 respectively (yı(t) corre-
sponding to rı). Find limt++20 yı(t) and limt7+ y2(t) for the following scenarios:
(a) a,b,c > 0
(b) a,c> 0 and b < 0 (c) a,b > 0) and c < 0. Assuming rı > 12
Let ri, r2 be the roots (real and distinct) of the characteristic equation of the homogeneous
differential equation
ay” + by’ + cy= 0
Write yı(t) and y2(t) i.e. the fundamental solutions in terms of rı, r2 respectively (yı(t) corre-
sponding to rı). Find limt++20 yı(t) and limt7+ y2(t) for the following scenarios:
(a) a,b,c > 0
(b) a,c> 0 and b < 0 (c) a,b > 0) and c < 0. Assuming rı > 12