Match the corresponding non-homogeneous equations with the corresponding types of solution considered by applying Undetermined coefficients. A. general solution of the homogneous equation: y(t)=c₁e¹+c₂te - cze ² cos e²cost +ce sint -✓y (4) + 2y (3) — 2y²-y=e¯ ✓y (4) + 2y (3) — 2y—y=3−1+1² y (4)- 2y (3) - 2y + 6y + 5y=e¹ y (4)-2y (3)-2y+6y + 5y=ecost one solution of the non-homogeneous equation of the form Y (1) = 1(Ae¹ cost + Be ²¹ sint) B. general solution of the homogenenous equation: -1 -1 y(t)=c₁_e¹+c₂e¹+cte +c ct²e solution of the non-homgeneous equation of the form: Y (1) = At³e¹ C. general solution of the homogeneous equation: y(t) = c )=c₁e¹+ solution of the non-homogeneous equation of the form : Y_(t) = A + Bt+Ct² D. general solution of the homogeneous equation: 2 y(t)=c₁₂e+c₂te -c₂e²cost +ce² sint one solution of the non-homogeneous equation of the form: Y (1) = 1²Ae¯¹
Match the corresponding non-homogeneous equations with the corresponding types of solution considered by applying Undetermined coefficients. A. general solution of the homogneous equation: y(t)=c₁e¹+c₂te - cze ² cos e²cost +ce sint -✓y (4) + 2y (3) — 2y²-y=e¯ ✓y (4) + 2y (3) — 2y—y=3−1+1² y (4)- 2y (3) - 2y + 6y + 5y=e¹ y (4)-2y (3)-2y+6y + 5y=ecost one solution of the non-homogeneous equation of the form Y (1) = 1(Ae¹ cost + Be ²¹ sint) B. general solution of the homogenenous equation: -1 -1 y(t)=c₁_e¹+c₂e¹+cte +c ct²e solution of the non-homgeneous equation of the form: Y (1) = At³e¹ C. general solution of the homogeneous equation: y(t) = c )=c₁e¹+ solution of the non-homogeneous equation of the form : Y_(t) = A + Bt+Ct² D. general solution of the homogeneous equation: 2 y(t)=c₁₂e+c₂te -c₂e²cost +ce² sint one solution of the non-homogeneous equation of the form: Y (1) = 1²Ae¯¹
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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Question
match with undet. coef.
Transcribed Image Text:Match the corresponding non-homogeneous equations with the corresponding types of solution considered by applying Undetermined coefficients.
A. general solution of the homogneous equation:
y (4)+ 2y (3) - 2y₁ - y=e
y(t)=c₁e
+c
✓y (4)+ 2y (3) - 2y -y=3-1+1²
(4) 2y (3) 2y
+ 6y +5y =e
y (4) – 2y (3) — 2y + 6y +5y=ecos t
2
cze
"cost +ce sint
one solution of the non-homogeneous equation of the form
2 sint)
Y (t) = t(Ae cost + Be
B. general solution of the homogenenous equation:
y (t) = c Le² + 2e
+czte
+c
solution of the non-homgeneous equation of the form: Y (1) = At³e¯¹
C. general solution of the homogeneous equation: y(t) = c.
c₁ e ² + c₂e
solution of the non-homogeneous equation of the form: Y (t) = A + Bt+Ct²
D. general solution of the homogeneous equation:
2
y(t) =c₁e +c
4⁰
cost+c sint
3e
one solution of the non-homogeneous equation of the form: Y (1) = 1²Ae¯¹
+
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