We consider the non-homogeneous problem y" - y' = 2x + 1 First we consider the homogeneous problem y" - y' = 0: 1) the auxiliary equation is ar² + br+c= m^2-r 2) The roots of the auxiliary equation are 0,1 3) A fundamental set of solutions is 1, e^x solution yc = C13/1 + 232 for arbitrary constants c₁ and ₂. = 0. (enter answers as a comma separated list). (enter answers as a comma separated list). Using these we obtain the the complementary Next we seek a particular solution y, of the non-homogeneous problem y" - y' = 2x + 1 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 complementary solution y = C131 + c2y2 and a particular solution: y = y + yp. Finally you are aske to use the general solution to solve an IVP. 5) Given the initial conditions y(0) = -2 and y' (0) = -3 find the unique solution to the IVP y =
We consider the non-homogeneous problem y" - y' = 2x + 1 First we consider the homogeneous problem y" - y' = 0: 1) the auxiliary equation is ar² + br+c= m^2-r 2) The roots of the auxiliary equation are 0,1 3) A fundamental set of solutions is 1, e^x solution yc = C13/1 + 232 for arbitrary constants c₁ and ₂. = 0. (enter answers as a comma separated list). (enter answers as a comma separated list). Using these we obtain the the complementary Next we seek a particular solution y, of the non-homogeneous problem y" - y' = 2x + 1 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 complementary solution y = C131 + c2y2 and a particular solution: y = y + yp. Finally you are aske to use the general solution to solve an IVP. 5) Given the initial conditions y(0) = -2 and y' (0) = -3 find the unique solution to the IVP y =
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' = 2x + 1
First we consider the homogeneous problem y" - y' = 0:
1) the auxiliary equation is ar² + br+c= M^2-r
2) The roots of the auxiliary equation are 0,1
3) A fundamental set of solutions is 1, e'x
solution y = C131 +232 for arbitrary constants c₁ and C₂.
= 0.
(enter answers as a comma separated list).
(enter answers as a comma separated list). Using these we obtain the the complementary
Next we seek a particular solution y, of the non-homogeneous problem y" - y' = 2x + 1 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 complementary solution y = C191 +₂32 and a particular solution: y = y + yp. Finally you are aske
to use the general solution to solve an IVP.
5) Given the initial conditions y(0) = -2 and y' (0) = -3 find the unique solution to the IVP
y =
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