We consider the non-homogeneous problem y" + y = 18 sin(2x) First we consider the homogeneous problem y" + y = 0: 1) the auxiliary equation is ar² + br+c= 2) The roots of the auxiliary equation are as a comma separated list). = 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" + y = 18 sin(2x) using the method of undetermined coefficients (See the link below for a help sheet) 4) Apply the method of undetermined coefficients to find yp = 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 5) Given the initial conditions y(0) = − 1 and y'(0) = −13 find the unique solution to the IVP
We consider the non-homogeneous problem y" + y = 18 sin(2x) First we consider the homogeneous problem y" + y = 0: 1) the auxiliary equation is ar² + br+c= 2) The roots of the auxiliary equation are as a comma separated list). = 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" + y = 18 sin(2x) using the method of undetermined coefficients (See the link below for a help sheet) 4) Apply the method of undetermined coefficients to find yp = 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 5) Given the initial conditions y(0) = − 1 and y'(0) = −13 find the unique solution to the IVP
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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Transcribed Image Text:We consider the non-homogeneous problem y" +y = 18 sin(2x)
First we consider the homogeneous problem y" + y = 0:
1) the auxiliary equation is ar² + br+c=
2) The roots of the auxiliary equation are
as a comma separated list).
= 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" + y = 18 sin(2x) using the method
of undetermined coefficients (See the link below for a help
sheet)
4) Apply the method of undetermined coefficients to find yp =
We then find the general solution as a sum of the comple-
mentary solution yc = C₁y1 +c2y2 and a particular solution:
y = Yc+yp. Finally you are asked to use the general solution
to solve an IVP.
5) Given the initial conditions y(0) = − 1 and y'(0) = −13 find the
unique solution to the IVP
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