Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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help me with part b and c please. thanks

 

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Consider the ODES x²y" - 2xy' + (x² + 2)y = 0, x²y" - 2xy' + (x² + 2)y x sin(x) Verify that y₁ = xcos(x) is a solution to ODE (2). (2) (3) b Find a fundamental set of solutions for the ODE (2), show they are indeed linearly independent, and identify the intervals on the real line where the Wronskian of this set of fundamental solutions is non-zero. Find the general solution of the ODE (3).
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Transcribed Image Text:Consider the ODES x²y" - 2xy' + (x² + 2)y = 0, x²y" - 2xy' + (x² + 2)y x sin(x) Verify that y₁ = xcos(x) is a solution to ODE (2). (2) (3) b Find a fundamental set of solutions for the ODE (2), show they are indeed linearly independent, and identify the intervals on the real line where the Wronskian of this set of fundamental solutions is non-zero. Find the general solution of the ODE (3).
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