- Solving 2nd-Order, Linear, Homogeneous ODES Given the 2nd-order, linear, homogeneous ODE y"(x) + P(x)y'(x) + Q(x)y(x) = 0, it can be shown that if the quantity Q'(x) + 2P(x)Q(xr) (Qx))3/2 Y = is a co. stant, then the transformation -Į JaQx) dx for any non-zero constant a will transform the original ODE to the ODE y"(2) + -Y'(2) + 금y(2) 3 0 which has constant coefficients. The solution to the original ODE is then y(x) = ¥(z) z = [ JaQ(x) dx. with Use this idea to determine a general solution to the following ODE 2xy" (x) + y'(x) + ly(x) = 0 for x > 0.

- Solving 2nd-Order, Linear, Homogeneous ODES Given the 2nd-order, linear, homogeneous ODE y"(x) + P(x)y'(x) + Q(x)y(x) = 0, it can be shown that if the quantity Q'(x) + 2P(x)Q(xr) (Qx))3/2 Y = is a co. stant, then the transformation -Į JaQx) dx for any non-zero constant a will transform the original ODE to the ODE y"(2) + -Y'(2) + 금y(2) 3 0 which has constant coefficients. The solution to the original ODE is then y(x) = ¥(z) z = [ JaQ(x) dx. with Use this idea to determine a general solution to the following ODE 2xy" (x) + y'(x) + ly(x) = 0 for x > 0.

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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