Consider the homogeneous differential equation x2y′′−3xy′+ 3y = 0, where x > 0. Complete the following four parts (a), (b), (c), and (d). (a) Show that y1(x) = x is a solution to the differential equation. (b) Show that y2(x) = x3 is a solution to the differential equation. (c) Show that y1 and y2 form a fundamental solution set. (d) Solve the initial value problem x2y′′−3xy′+ 3y = 0; y(1) = 0, y′(1) = −2.
Consider the homogeneous differential equation x2y′′−3xy′+ 3y = 0, where x > 0. Complete the following four parts (a), (b), (c), and (d). (a) Show that y1(x) = x is a solution to the differential equation. (b) Show that y2(x) = x3 is a solution to the differential equation. (c) Show that y1 and y2 form a fundamental solution set. (d) Solve the initial value problem x2y′′−3xy′+ 3y = 0; y(1) = 0, y′(1) = −2.
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 homogeneous
x2y′′−3xy′+ 3y = 0, where x > 0.
Complete the following four parts (a), (b), (c), and (d).
(a) Show that y1(x) = x is a solution to the differential equation.
(b) Show that y2(x) = x3 is a solution to the differential equation.
(c) Show that y1 and y2 form a fundamental solution set.
(d) Solve the initial value problem
x2y′′−3xy′+ 3y = 0; y(1) = 0, y′(1) = −2.
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