Page 24 - Schaum's Outline of Differential Equations

CHAP.1] BASIC CONCEPTS 7

1.26. Which of the following functions are solutions of the differential equation y — 2ty = f!
2
(a) y = 2, (b) y = -\, (c) y = e'\ (d) y = e' -±, (e) y = -1/-\
1.27. Which of the following functions are solutions of the differential equation dyldt = yltl
(a) y = 0, (b) y = 2, (c) y = 2t, (d) y = -3t, (e) y = t 2

1.28. Which of the following functions are solutions of the differential equation

1.29. Which of the following functions are solutions of the differential equation y" -y = 0?
x
(a) y = e", (b) y = sin x, (c) y = 4e , (d) y = 0,
1.30. Which of the following functions are solutions of the differential equation y" — xy' + y = Ql
2
2
2
(a) y = x , (b) y = x, (c) y=l-x , (d) y = 2x - 2, (e) y = 0
1.31. Which of the following functions are solutions of the differential equation x - 4x + 4x = e'
2
2
2t
2t
(a) x = e', (b) x = e ', (c) x = e + e', (d) x= te ' + e', (e) x = e + te'
2t
In Problems 1.32 through 1.35, find c so that x(t) = ce satisfies the given initial condition.
1.32. X0) = 0 1.33. X0)=l 1.34. XI) =1 1-35. x(2) = -3

In Problems 1.36 through 1.39, hnd c so that y(x) = c(\- x) satishes the given initial condition.

1.36. XO) = 1 1-37. XI) = 0 1.38. y(2) = 1 1.39. XI) = 2

In Problems 1.40 through 1.49, find c 1 and c 2 so that y(x) = c 1 sin x + c 2 cos x will satisfy the given conditions
Determine whether the given conditions are initial conditions or boundary conditions.

1.40. XO) = 1, /(O) = 2 1.41. XO) = 2, y'(0) = 1

1.45. XO) = 1, Y(ri) = 1

1.46. XO) = 1, XTC) = 2 1.47. XO) = 0, /(O) = 0