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We consider the non-homogeneous problem y″ = 12 (2x² — 12x) First we consider the homogeneous problem y" = 0: 1) the auxiliary equation is ar² +br+c= 2) The roots of the auxiliary equation are. as a comma separated list). 0. 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. (enter answers Next we seek a particular solution yp of the non- homogeneous problem y" = 12 (2x² — 12x) using the method of undetermined coefficients (See the link below for a help sheet) 4) Apply the method of undetermined coefficients to find yp = 5) Given the initial conditions y(0) : unique solution to the IVP 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. y = 1 and y' (0) -2 find the

We consider the non-homogeneous problem y″ = 12 (2x² — 12x) First we consider the homogeneous problem y" = 0: 1) the auxiliary equation is ar² +br+c= 2) The roots of the auxiliary equation are. as a comma separated list). 0. 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. (enter answers Next we seek a particular solution yp of the non- homogeneous problem y" = 12 (2x² — 12x) using the method of undetermined coefficients (See the link below for a help sheet) 4) Apply the method of undetermined coefficients to find yp = 5) Given the initial conditions y(0) : unique solution to the IVP 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. y = 1 and y' (0) -2 find the

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″ = 12 (2x² — 12x) First we consider the homogeneous problem y" = 0 : 1) the auxiliary equation is ar² +br+c= 2) The roots of the auxiliary equation are. as a comma separated list). 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. = 0. Next we seek a particular solution yp of the non- homogeneous problem y” = 12 (2x² — 12x) using the method of undetermined coefficients (See the link below for a help sheet) 4) Apply the method of undetermined coefficients to find yp = 5) Given the initial conditions y(0) : unique solution to the IVP (enter answers 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. y = 1 and y' (0) -2 find the ==
Transcribed Image Text:We consider the non-homogeneous problem y″ = 12 (2x² — 12x) First we consider the homogeneous problem y" = 0 : 1) the auxiliary equation is ar² +br+c= 2) The roots of the auxiliary equation are. as a comma separated list). 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. = 0. Next we seek a particular solution yp of the non- homogeneous problem y” = 12 (2x² — 12x) using the method of undetermined coefficients (See the link below for a help sheet) 4) Apply the method of undetermined coefficients to find yp = 5) Given the initial conditions y(0) : unique solution to the IVP (enter answers 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. y = 1 and y' (0) -2 find the ==
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