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- (a) Show that 2x°y" + (cos 2x - 1)y' +2xy = 0 has only one Frobenius series solution. %3D (b) Verify that the origin is a regular singular point of the differential equation 2x²y" +3xy' - (x² +1)y = 0 and then calculate two independent Frobenius series solution of the given equation.

- (a) Show that 2x°y" + (cos 2x - 1)y' +2xy = 0 has only one Frobenius series solution. %3D (b) Verify that the origin is a regular singular point of the differential equation 2x²y" +3xy' - (x² +1)y = 0 and then calculate two independent Frobenius series solution of the given equation.

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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6. (a) Show that 2x°y" + (cos 2x 1)y' + 2xy = 0 has only one Frobenius series solution. (b) Verify that the origin is a regular singular point of the differential equation 2x?y" +3xy' – (x²+1)y = 0 %3D and then calculate two independent Frobenius series solution of the given equation.
Transcribed Image Text:6. (a) Show that 2x°y" + (cos 2x 1)y' + 2xy = 0 has only one Frobenius series solution. (b) Verify that the origin is a regular singular point of the differential equation 2x?y" +3xy' – (x²+1)y = 0 %3D and then calculate two independent Frobenius series solution of the given equation.
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