Un-1 n=3,4,... & a1 =a0.a2=(1+ag)is theIf an=recurrence relation of y'-x -y = 0, then the power series solution isy = ao + a, x + a2x +....= ao + aox + (1+ ao)M%3Dn=0 n!y = 90-a1 x- azx²+.°0 - 9g* - (1+ ao) En=on!....1o + ag* + (1 + ac) En=o n!x ++%3D....V=-0+a x+ azx².-9o + 9o* + (1 + a,)En=on!+....

Let y=∑n=0∞anxn be the series solution Given: a1=a0, a2=1+a02, an=an-1n , n=3, 4,....

(1+a) Un-1.n=3,4,.... & a1 =a0.a2=* If an = is the recurrence relation of y'-x-y= 0, then the power series solution is y = ao + a, x+ azx? +....= ao + ax+ (1 + a) E- = ao + acx + (1 + a») Ex" %3D y= a0-a1 x-azx²+....= a0 - aox- (1+ a) E n=on! 1 - °o + °o* + (1 + a,) %3D Σ n=on! ... 1 o + °g* + (1 + ao)_ n=on! x + ....

(1+a) Un-1.n=3,4,.... & a1 =a0.a2=* If an = is the recurrence relation of y'-x-y= 0, then the power series solution is y = ao + a, x+ azx? +....= ao + ax+ (1 + a) E- = ao + acx + (1 + a») Ex" %3D y= a0-a1 x-azx²+....= a0 - aox- (1+ a) E n=on! 1 - °o + °o* + (1 + a,) %3D Σ n=on! ... 1 o + °g* + (1 + ao)_ n=on! x + ....

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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