Consider the linear ODE 2°y(3) + 6x?y" + 4xy' – 4y = 0 -2 and In x are solutions to the ODE and their Wronskian is non-zero (i.e., they are linearly (a) Verify that y1 = x, Y2 = x Y3 = x independent). (b) Solve the initial value problem with initial conditions: y(1) = 1, y'(1) = 5, y"(1) = -11.

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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Consider the linear ODE
2³y(3) + 6x²y" + 4xy' – 4y = 0
(a) Verify that Y1 = x, Y2 = x
and
Y3 = x
In x are solutions to the ODE and their Wronskian is non-zero (i.e., they are linearly
independent).
(b) Solve the initial value problem with initial conditions:
y(1) = 1, y'(1) = 5, y" (1) = -11.
Transcribed Image Text:Consider the linear ODE 2³y(3) + 6x²y" + 4xy' – 4y = 0 (a) Verify that Y1 = x, Y2 = x and Y3 = x In x are solutions to the ODE and their Wronskian is non-zero (i.e., they are linearly independent). (b) Solve the initial value problem with initial conditions: y(1) = 1, y'(1) = 5, y" (1) = -11.
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