hird-order Euler equation is one of the form ax y"" + bxʻy" + cxy' + ky = 0, where a, b, c, and k are constant n the substitution v= In x transforms the equation into the constant coefficient linear equation below, with inc iable v. d°y + (b- За) dv d?y + (с-b+ 2a) dv? dy + ky = 0 a- ke the substitution v = In x to find the general solution of x°y'"' + 9x0.
hird-order Euler equation is one of the form ax y"" + bxʻy" + cxy' + ky = 0, where a, b, c, and k are constant n the substitution v= In x transforms the equation into the constant coefficient linear equation below, with inc iable v. d°y + (b- За) dv d?y + (с-b+ 2a) dv? dy + ky = 0 a- ke the substitution v = In x to find the general solution of x°y'"' + 9x0.
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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Transcribed Image Text:A third-order Euler equation is one of the form ax°y'' + bx-y'" + cxy' + ky = 0, where a, b, c, and k are constants. If x > 0,
then the substitution v = In x transforms the equation into the constant coefficient linear equation below, with independent
variable v.
d°y
d²y
+ (с -b+2a)-
dv?
dy
+ ky = 0
dv
a
+ (b - За)-
3
dv
Make the substitution v = In x to find the general solution of x y"" + 9xy'" + 19xy' + 8y = 0 for x> 0.
y(x) =|
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