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9. Second order ODE a) Consider the following nonhomogeneous ODEs, find their homogeneous solution, and give the form (no need to determine coefficients) of nonhomogeneous solution. i) 4y" + 12y' + 13y=32e-¹.5x sin(x)+cos(x) ii) y" + 6y' +9y=4x cosh(3x) b) Find the general solution of y" + Ay'=3e¯ where A is a real constant with following steps i) Deter- mine homogeneous solution, ii) Find nonhomogeneous solut ion with coefficients determined using the method of undetermined coefficients and iii) Arrive at the general solution.

9. Second order ODE a) Consider the following nonhomogeneous ODEs, find their homogeneous solution, and give the form (no need to determine coefficients) of nonhomogeneous solution. i) 4y" + 12y' + 13y=32e-¹.5x sin(x)+cos(x) ii) y" + 6y' +9y=4x cosh(3x) b) Find the general solution of y" + Ay'=3e¯ where A is a real constant with following steps i) Deter- mine homogeneous solution, ii) Find nonhomogeneous solut ion with coefficients determined using the method of undetermined coefficients and iii) Arrive at the general solution.

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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9. Second order ODE a) Consider the following nonhomogeneous ODEs, find their homogeneous solution, and give the form (no need to determine coefficients) of nonhomogeneous solution. i) 4y" + 12y' + 13y=32e-¹.5x sin(x)+cos(x) ii) y" + 6y' +9y=4x cosh(3x) b) Find the general solution of y" + Ay'=3e¯ where A is a real constant with following steps i) Deter- mine homogeneous solution, ii) Find nonhomogeneous solut ion with coefficients determined using the method of undetermined coefficients and iii) Arrive at the general solution.
Transcribed Image Text:9. Second order ODE a) Consider the following nonhomogeneous ODEs, find their homogeneous solution, and give the form (no need to determine coefficients) of nonhomogeneous solution. i) 4y" + 12y' + 13y=32e-¹.5x sin(x)+cos(x) ii) y" + 6y' +9y=4x cosh(3x) b) Find the general solution of y" + Ay'=3e¯ where A is a real constant with following steps i) Deter- mine homogeneous solution, ii) Find nonhomogeneous solut ion with coefficients determined using the method of undetermined coefficients and iii) Arrive at the general solution.
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