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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.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 69EQ: Let x=x(t) be a twice-differentiable function and consider the second order differential equation...
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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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