(a) Show that the following Euler equation can be transformed into a 2nd order ODE with constant coefficients by letting x=e'. x²y" + pxy' + qy = 0. where p and q are real constants. (b) Find the general solution of the following equation where x > 0. х?у" + 5ху' + 4.25у %3D 0. ||

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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(a) Show that the following Euler equation can be transformed into a 2nd order ODE with constant
coefficients by letting x=e'.
х2у" + рху' + qy %3D 0.
where p and
q are real constants.
(b) Find the general solution of the following equation where x > 0.
х?у" + 5ху' + 4.25у %3D 0.
||
Transcribed Image Text:(a) Show that the following Euler equation can be transformed into a 2nd order ODE with constant coefficients by letting x=e'. х2у" + рху' + qy %3D 0. where p and q are real constants. (b) Find the general solution of the following equation where x > 0. х?у" + 5ху' + 4.25у %3D 0. ||
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