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Use variation of parameters (D²+1) y = 4 sec x

Use variation of parameters (D²+1) y = 4 sec 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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Can you solve this equation using the given flow for the variation of parameters?

1. Use variation of parameters

(D2+1) y=sec4x

1. Use variation of parameters (D²+1) y = sec^x 4
Transcribed Image Text:1. Use variation of parameters (D²+1) y = sec^x 4
Solve the differential equation (D²-1)y=e+1 Solution: First we get the complementary solution, the roots are m - 11 the complementary solution is + Let the particular solution be =Ae+Be* differentiating-A-Be+Ae+80* we set A'e² +8 -0, thus - As-Be* 3+B+Ae-We substituting to the given equation A+Be+A-8-A-B²+1 cancelling like terms, we have A-8=e+1 however A=-8'e which we substitute +1 8=- solving for B by integration, B=-e-fe² next we solve for A 2²-²+1 integrate to solve for A substitute the value of A and B to the equation % Ae+Be = the general solution is y=y+% y = ge* +*+*-*-1
Transcribed Image Text:Solve the differential equation (D²-1)y=e+1 Solution: First we get the complementary solution, the roots are m - 11 the complementary solution is + Let the particular solution be =Ae+Be* differentiating-A-Be+Ae+80* we set A'e² +8 -0, thus - As-Be* 3+B+Ae-We substituting to the given equation A+Be+A-8-A-B²+1 cancelling like terms, we have A-8=e+1 however A=-8'e which we substitute +1 8=- solving for B by integration, B=-e-fe² next we solve for A 2²-²+1 integrate to solve for A substitute the value of A and B to the equation % Ae+Be = the general solution is y=y+% y = ge* +*+*-*-1
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