In this problem you will use variation of parameters to solve the nonhomogeneous equation y" - 2y + y = -6e¹ This DE is in the standard form y" + P(t)y' + Q(t)y= g(t). A. Write the characteristic equation for the associated homogeneous equation. (Usem for your variable.) 0 B. Write the fundamental solutions for the associated homogeneous equation and their Wronskian. W(31,2)= U2 = Y1 = -21= C. Compute the following integrals. (In the differential equation, g(t) = -6et is the "forcing function".) I sw d J W D. Write the general solution. (Use c1 and c2 for C₁ and ₂). Y = = dt= Y29 Y2 -dt (Note: Your general solution will only be correct if it is a general solution to the differential equation.)
In this problem you will use variation of parameters to solve the nonhomogeneous equation y" - 2y + y = -6e¹ This DE is in the standard form y" + P(t)y' + Q(t)y= g(t). A. Write the characteristic equation for the associated homogeneous equation. (Usem for your variable.) 0 B. Write the fundamental solutions for the associated homogeneous equation and their Wronskian. W(31,2)= U2 = Y1 = -21= C. Compute the following integrals. (In the differential equation, g(t) = -6et is the "forcing function".) I sw d J W D. Write the general solution. (Use c1 and c2 for C₁ and ₂). Y = = dt= Y29 Y2 -dt (Note: Your general solution will only be correct if it is a general solution to the differential equation.)
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:In this problem you will use variation of parameters to solve the nonhomogeneous equation
y" - 2y + y = -6e¹
This DE is in the standard form y" + P(t)y' + Q(t)y = g(t).
A. Write the characteristic equation for the associated homogeneous equation. (Usem for your variable.)
B. Write the fundamental solutions for the associated homogeneous equation and their Wronskian.
W (y1, y2)
U2 =
Y1 =
C. Compute the following integrals. (In the differential equation, g(t) = -6e* is the "forcing function".)
Y19
[
-U1=
y =
Y2 =
dt
Y29
/dt = 0
-dt
W
D. Write the general solution. (Use c1 and c2 for C₁ and ₂).
(Note: Your general solution will only be correct if it is a general solution to the differential equation.)
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