Homework #3 Math 527
Follow the usual instructions on homework submission: Be clear, legible, and organized.
Write on loose-leaf paper. Staple together in the left-hand corner, write your name,
section #, Math 527 HW2, and date in the upper-right-hand corner.
Problems 1-6. Find the general solution of the differential equation using judicious
guessing. The “prime” notation indicates differentiation with respect to x or t, whichever
appears on the right-hand-side.
1. y00 + 3y = x
3 − 1
2. y00 + 4y
0 + 4y = te2t
3. y00 + 2y
0 + y = e
−t
4. y00 + 4y = tsin 2t
5. y00 − 2y
0 + 5y = 2 cos2 x
6. y00 + y
0 − 6y = sin t + te2t
Problem 7. Solve the initial value problem
y
00 − y = cosh x; y(0) = 2, y0
(0) = 12
