Match the following guess solutions yp for the method of undetermined coefficients with the second-order nonhomogeneous linear equations below. A. yp(x) = Ax² + Bx + C, + Bx + C, B. yp(x) = Ae²x, C. Yp(x) = A cos 2x + B sin 2x, D. Yp(x) = (Ax + B) cos 2x + (Cx + D) sin 2x E. Yp(x) = Axe², and F. 1. 2. 3. 4. 3x Yp(x) = e³¹ (A cos 2x + B sin 2x) d²y dx² d²y dx² + 4y = x dy dx +6. y" + 4y + 13y x² + 8y = e2x = 20 3 cos 2x y" - 2y - 15y = e cos 2x
Match the following guess solutions yp for the method of undetermined coefficients with the second-order nonhomogeneous linear equations below. A. yp(x) = Ax² + Bx + C, + Bx + C, B. yp(x) = Ae²x, C. Yp(x) = A cos 2x + B sin 2x, D. Yp(x) = (Ax + B) cos 2x + (Cx + D) sin 2x E. Yp(x) = Axe², and F. 1. 2. 3. 4. 3x Yp(x) = e³¹ (A cos 2x + B sin 2x) d²y dx² d²y dx² + 4y = x dy dx +6. y" + 4y + 13y x² + 8y = e2x = 20 3 cos 2x y" - 2y - 15y = e cos 2x
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:Match the following guess solutions yp for the method of
undetermined coefficients with the second-order
nonhomogeneous linear equations below.
Ax² + Bx + C, B. yp(x) = Ae²x, C.
Yp(x) = A cos 2x + B sin 2x,
D. yp(x) = (Ax + B) cos 2x + (Cx + D) sin 2x E.
Yp(x) = Axe²x, and F.
A. Yp(x) = Ax²
1.
2.
3.
4.
3x
Yp(x) = e³¹ (A cos 2x + B sin 2x)
d²y
dx²
+ 4y = x
dy
dx
x²
d²y
dx²
y" + 4y + 13y = 3 cos 2x
+ 6-
20
+ 8y = e²x
3x
y" - 2y' - 15y = e³ cos 2x
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