Download Differential Equations, Winter 07 Grinshpan QUIZ 3 Answers A) The

Differential Equations, Winter 07
Grinshpan
QUIZ 3 Answers
A) The characteristic equation for 2y 00 (x) − 3y 0 (x) + y(x) = 0 is
2r2 − 3r + 1 = 0. It has roots r1 = 1 and r2 = 21 . Hence y = c1 ex + c2 ex/2 is
the general solution. To match y(0) = 2 and y 0 (0) = 21 we need c1 + c2 = 2 and
c1 + 21 c2 = 12 . Hence c1 = −1 and c2 = 3.
B) To find an equation ay 00 + by 0 + cy = 0 whose general solution is
y = c1 ex + c2 note that r1 = 1 and r2 = 0. So the characteristic equation must
be (r − 1)(r − 0) = r2 − r = 0. Hence y 00 − y 0 = 0 is the corresponding equation.