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3. Consider the non-Sturm-Liouville differential equation 4" (x) + a(x)o'(x) + [AB(x) + y(x)]ø(x) = 0. %3D Multiply this equation by H(r). Determine H(x) such that the equation may be reduced to the standard Sturm-Liouvill form: [p(x)o'(x)]' + [Ao(x) + p(x)]ø(x) = 0. Given a(x), B(r) and y(x), what are p(r), o(x) and q(x)? Hint. Recall the method of integrating factor for ordinary differential equations.

3. Consider the non-Sturm-Liouville differential equation 4" (x) + a(x)o'(x) + [AB(x) + y(x)]ø(x) = 0. %3D Multiply this equation by H(r). Determine H(x) such that the equation may be reduced to the standard Sturm-Liouvill form: [p(x)o'(x)]' + [Ao(x) + p(x)]ø(x) = 0. Given a(x), B(r) and y(x), what are p(r), o(x) and q(x)? Hint. Recall the method of integrating factor for ordinary differential equations.

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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3. Consider the non-Sturm-Liouville differential equation " (x) + a(x)o'(x) + [AB(x) +y(x)]o(x) = 0. Multiply this equation by H(x). Determine H(x) such that the equation may be reduced to the standard Sturm-Liouvill form: [p(x)o(r)]' + [Ao(x)+ p(x)]ø(x) = 0. Given a(x), B(x) and y(x), what are p(x), o(x) and q(x)? Hint. Recall the method of integrating factor for ordinary differential equations.
Transcribed Image Text:3. Consider the non-Sturm-Liouville differential equation " (x) + a(x)o'(x) + [AB(x) +y(x)]o(x) = 0. Multiply this equation by H(x). Determine H(x) such that the equation may be reduced to the standard Sturm-Liouvill form: [p(x)o(r)]' + [Ao(x)+ p(x)]ø(x) = 0. Given a(x), B(x) and y(x), what are p(x), o(x) and q(x)? Hint. Recall the method of integrating factor for ordinary differential equations.
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