Page 269 - Schaum's Outline of Differential Equations

252 SOLUTIONS OF LINEAR SYSTEMS BY LAPLACE TRANSFORMS [CHAP. 25

Solving this last system for Z(s) and Y(s), we find that

Finally, taking inverse transforms, we obtain

25.6. Solve the system

Taking Laplace transforms of all three differential equations, we find that

or

The solution to this system is

Hence,

Supplementary Problems

Use Laplace transforms to solve the following systems. All unknowns are functions of x.

25.7. u'-2v = 3 25.8. u' + 4u-6v=0
2
v' + v —u =-x ; v' + 3u-5v=0;
u(0) = 0, v(0) = -1 u(0) = 3, v(0) = 2

25.9. M' + 5M-12v=0 25.10. y + z=x
v' + 2u-5v=0; z'-y=0;

u(0) = 8, v(0) = 3 X0)=l,z(0) = 0