1. Solve the differential equation e2 d = e-y- 2xe3-y. 2. Solve the differential equation x- 2y = x cos() on (0, o). 3. Show that the differential equation (1– 2y + x In r)da + (ev- 2a)dy = 0 is exact and find its solutions. 4. Solve (1- ²)y" + 2xy' - 2y = 0 on (-1, 1) given that y1 = x is a solution. 5. (a) Solve the initial-value problem 2y" + y'-y = 0, y(0) = 0, y'(0) = 1. (b) Solve the differential equation y"+ 4y'+8y = 0.
1. Solve the differential equation e2 d = e-y- 2xe3-y. 2. Solve the differential equation x- 2y = x cos() on (0, o). 3. Show that the differential equation (1– 2y + x In r)da + (ev- 2a)dy = 0 is exact and find its solutions. 4. Solve (1- ²)y" + 2xy' - 2y = 0 on (-1, 1) given that y1 = x is a solution. 5. (a) Solve the initial-value problem 2y" + y'-y = 0, y(0) = 0, y'(0) = 1. (b) Solve the differential equation y"+ 4y'+8y = 0.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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