Apply the method of undetermined coefficients to find y₂ = We then find the general solution as a sum of the complementary solution y = C131 + C292 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) = -1 and y'(0) = -36 find the unique solution to the IVP
Apply the method of undetermined coefficients to find y₂ = We then find the general solution as a sum of the complementary solution y = C131 + C292 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) = -1 and y'(0) = -36 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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We consider the non-homogeneous problem y"+y'-6y = 50(2x + 3)e-3
First we consider the homogeneous problem y' + y - 6y=0:
1) the auxiliary equation is ar2 + br+c=2+r-6=0.
2) The roots of the auxiliary equation are -3,2 (enter answers as a comma separated list).
-3x
3) A fundamental set of solutions is
e e²x
(enter answers as a comma separated list). Using these we obtain the the
complementary solution ye C1y1 + C2y2 for arbitrary constants c₁ and c₂.
Next we seek a particular solution y, of the non-homogeneous problem y"+y-6y=50(2x + 3)e-3 using the method of
undetermined coefficients (See the link below for a help sheet)
4) Apply the method of undetermined coefficients to find y₂ =
0
We then find the general solution as a sum of the complementary solution ye = C1y1 + C292 and a particular solution:
y = y + 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) = -36 find the unique solution to the IVP
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Help Sheet: Undetermined Coefficients Notes
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DOLL
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