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4) Derive the general solution of the following differential equations: dy (x-1). -x- -+y = f(x) dx² dx and specialize your result for the case f(x)=1. Hint: Verify that y=e* is a solution of the homogeneous equation. i) ii) d'y (cos²x)-2y = f(x) dx and specialize your result for the case f(x)=cosx. Hint: Verify that y = tanx is a solution of the homogeneous equation.

4) Derive the general solution of the following differential equations: dy (x-1). -x- -+y = f(x) dx² dx and specialize your result for the case f(x)=1. Hint: Verify that y=e* is a solution of the homogeneous equation. i) ii) d'y (cos²x)-2y = f(x) dx and specialize your result for the case f(x)=cosx. Hint: Verify that y = tanx is a solution of the homogeneous equation.

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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4) Derive the general solution of the following differential equations: i) (x-1)- dy --x+y=f(x) dx dx² and specialize your result for the case f(x)=1. Hint: Verify that y=e* is a solution of the homogeneous equation. ii) y d²y (cos²x)-2y = f(x) dx and specialize your result for the case f(x)=cosx. Hint: Verify that y = tan x is a solution of the homogeneous equation.
Transcribed Image Text:4) Derive the general solution of the following differential equations: i) (x-1)- dy --x+y=f(x) dx dx² and specialize your result for the case f(x)=1. Hint: Verify that y=e* is a solution of the homogeneous equation. ii) y d²y (cos²x)-2y = f(x) dx and specialize your result for the case f(x)=cosx. Hint: Verify that y = tan x is a solution of the homogeneous equation.
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