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Consider the second order homogeneous equation: 2x°y" +3.xy' – y = 0, (x>0) (a) Verify that y, =xV² and y, =x' are solutions of the ODE. (b) Find the Wronskian, W(y,,y,). (c) Do y, and y, form a fundamental set of solutions for the given ODE? If so, state the general solution.

Consider the second order homogeneous equation: 2x°y" +3.xy' – y = 0, (x>0) (a) Verify that y, =xV² and y, =x' are solutions of the ODE. (b) Find the Wronskian, W(y,,y,). (c) Do y, and y, form a fundamental set of solutions for the given ODE? If so, state the general solution.

Advanced Engineering Mathematics
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 second order homogeneous equation: 2x°y" +3.xy' – y = 0, (x>0) (a) Verify that y, =xV² and y, =x' are solutions of the ODE. (b) Find the Wronskian, W(y,,y,). (c) Do y, and y, form a fundamental set of solutions for the given ODE? If so, state the general solution.
Transcribed Image Text:Consider the second order homogeneous equation: 2x°y" +3.xy' – y = 0, (x>0) (a) Verify that y, =xV² and y, =x' are solutions of the ODE. (b) Find the Wronskian, W(y,,y,). (c) Do y, and y, form a fundamental set of solutions for the given ODE? If so, state the general solution.
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