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We consider the non-homogeneous problem y" +6y' +13y = 180 sin(x)

We consider the non-homogeneous problem y" +6y' +13y = 180 sin(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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We consider the non-homogeneous problem y"+6y' +13y = 180 sin(x) First we consider the y" + 6y + 13y = 0: 1) the auxiliary equation is ar² + br+c= 2) The roots of the auxiliary equation are as a comma separated list). homogeneous problem 0. (enter answers 3) A fundamental set of solutions is (enter answers as a comma separated list). Using these we obtain the the comple- mentary solution yc = C1y1 + c2y2 for arbitrary constants c₁ and C2. Next we seek a particular solution yp of the non- homogeneous problem y" +6y' + 13y = 180 sin(x) using the method of undetermined coefficients (See the link below for a help sheet) = 4) Apply the method of undetermined coefficients to find yp y = We then find the general solution as a sum of the comple- mentary solution yc = C₁y1 +C2y2 and a particular solution: y = ye+yp. Finally you are asked to use the general solution to solve an IVP. 5) Given the initial conditions y(0) = −6 and y'(0) = 14 find the unique solution to the IVP
Transcribed Image Text:We consider the non-homogeneous problem y"+6y' +13y = 180 sin(x) First we consider the y" + 6y + 13y = 0: 1) the auxiliary equation is ar² + br+c= 2) The roots of the auxiliary equation are as a comma separated list). homogeneous problem 0. (enter answers 3) A fundamental set of solutions is (enter answers as a comma separated list). Using these we obtain the the comple- mentary solution yc = C1y1 + c2y2 for arbitrary constants c₁ and C2. Next we seek a particular solution yp of the non- homogeneous problem y" +6y' + 13y = 180 sin(x) using the method of undetermined coefficients (See the link below for a help sheet) = 4) Apply the method of undetermined coefficients to find yp y = We then find the general solution as a sum of the comple- mentary solution yc = C₁y1 +C2y2 and a particular solution: y = ye+yp. Finally you are asked to use the general solution to solve an IVP. 5) Given the initial conditions y(0) = −6 and y'(0) = 14 find the unique solution to the IVP
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