Page 270 - Schaum's Outline of Differential Equations

CHAP. 25] SOLUTIONS OF LINEAR SYSTEMS BY LAPLACE TRANSFORMS 253

25.11. y-z=0 25.12. w'-w-2y = l
y-z' = o- y' _4 W -3-y = _l ;

y(0) = 1, z(0) = 1 w(0) = 1, XO) = 2

25.13. w'-y=0 25.14. u" + v = Q

W + y' + Z = l u" -v' = -2e";

w - y + z' = 2 sin x; u(0) = 0, u'(0) = -2, v(0) = 0, v'(0) = 2
w(0) = 1,XO) = l,z(0) = 1

25.15. M"-2v = 2 25.16. w"-2z=0

2x
u + v' = 5e +l; w' + y' -z = 2x
u(0) = 2, u'(0) = 2, v(0) = 1 w' -2y+i"=0;
W(Q) = 0, w'(0) = 0, XO) = 0,

Z(0) = l,z'(0) = 0

25.17. w" + y+z=-\
w+y" -i=0

-w'-y' + z" = 0;
w(0) = 0, w'(0) = 1, XO) = 0,

/(0) = 0, z(0) = -l,z'(0) = l