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Consider the differential equation: 4x 4x²d²y. dy dx² +4x +(16x²-1)y=x dx which has the following two linearly independent solution of the homogineous equation cos(2x) sin(2x) V/₁ = ,V/₂= √2x √2x The particular solution is given by: 1 Yp(x)= 2x Yp(x)= cos(2x)sin(2x) 4√x 2cos(2x)sin(2x) Yp(x)= √2x cos(2x) sin(2x) Yp(x)= + √2x √2x , (x) 16√√x

Consider the differential equation: 4x 4x²d²y. dy dx² +4x +(16x²-1)y=x dx which has the following two linearly independent solution of the homogineous equation cos(2x) sin(2x) V/₁ = ,V/₂= √2x √2x The particular solution is given by: 1 Yp(x)= 2x Yp(x)= cos(2x)sin(2x) 4√x 2cos(2x)sin(2x) Yp(x)= √2x cos(2x) sin(2x) Yp(x)= + √2x √2x , (x) 16√√x

Advanced Engineering Mathematics
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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Consider the differential equation: 4x 4x²d²y. dy dx² +4x +(16x²-1)y=x dx which has the following two linearly independent solution of the homogineous equation cos(2x) sin(2x) V/₁ = ,V/₂= √2x √2x The particular solution is given by: 1 Yp(x)= 2x Yp(x)= cos(2x)sin(2x) 4√x 2cos(2x)sin(2x) Yp(x)= √2x cos(2x) sin(2x) Yp(x)= + √2x √2x , (x) * 16√√x
Transcribed Image Text:Consider the differential equation: 4x 4x²d²y. dy dx² +4x +(16x²-1)y=x dx which has the following two linearly independent solution of the homogineous equation cos(2x) sin(2x) V/₁ = ,V/₂= √2x √2x The particular solution is given by: 1 Yp(x)= 2x Yp(x)= cos(2x)sin(2x) 4√x 2cos(2x)sin(2x) Yp(x)= √2x cos(2x) sin(2x) Yp(x)= + √2x √2x , (x) * 16√√x
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