Page 130 - Schaum's Outline of Differential Equations

CHAP. 13] INITIAL-VALUE PROBLEMS 113

Applying the second initial condition, we obtain

or

Solving (_/) and (2) simultaneously, we find that

whereupon, the solution to the initial-value problem becomes

Supplementary Problems

Solve the following initial-value problems.

3x
13.7. /' -y'-2y = e ; y(G) = 1, /(O) = 2
3x
13.8. /' -y'-2y = e ; y(G) = 2, /(O) = 1
13.9. /' -y'-2y = 0; y(0) = 2, /(O) = 1
3x
13.10. /' ~y'-2y = e ; (l) = 2, /(I) = 1
y
13.11. /' + y = x; XI) = 0, /(!) = !

2
13.12. /' + 4y = sin 2x; y(n) = 0, y'(n) = 0
13.13. y" + y = 0;y(2) = 0,y'(2) = 0

13.14. y'" = 12; XI) = 0, /(I) = 0, /'(I) = 0

13.15. y = 2y+ 2y = sin 2t + cos 2t; y(0) = 0, y(0) = 1