the following Cauchy-Euler equation: 9x2y′′−9xy′+9y=0 (1) Write the corresponding characteristic equation using the variable m: ....?.....=0. Note: do not simplify the coefficients. (2) Write the general solution with c1 and c2 arbitrary constants: y(x)=c1 y1(x)+c2 y2(x)=c1....?.....+c2....?. ... (3) Finally, write the solution of the following initial value problem. 9x2y′′−9xy′+9y=0, y(1)=4, y′(1)=−5. y(x)=?
the following Cauchy-Euler equation: 9x2y′′−9xy′+9y=0 (1) Write the corresponding characteristic equation using the variable m: ....?.....=0. Note: do not simplify the coefficients. (2) Write the general solution with c1 and c2 arbitrary constants: y(x)=c1 y1(x)+c2 y2(x)=c1....?.....+c2....?. ... (3) Finally, write the solution of the following initial value problem. 9x2y′′−9xy′+9y=0, y(1)=4, y′(1)=−5. y(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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Solve the following Cauchy-Euler equation:
9x2y′′−9xy′+9y=0
(1) Write the corresponding characteristic equation using the variable m:
....?.....=0.
Note: do not simplify the coefficients.
(2) Write the general solution with c1 and c2 arbitrary constants: y(x)=c1 y1(x)+c2 y2(x)=c1....?.....+c2....?. ...
(3) Finally, write the solution of the following initial value problem.
9x2y′′−9xy′+9y=0, y(1)=4, y′(1)=−5.
y(x)=?
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