If C₁ * x² = c(1) ²¹ + a₂ (1) ²³ t² is the complementary solution of the nonhomogeneous system 3 (21), 2-2 then the particular solution of the system is 3 1 YO=(1) + + + (17) +- (31/2₂) 10 a) x² 1 b) x² (0)-(2) + (1)-(3/2) (t)= 10 ©) x²(1) - 1 (7²)^*-(312) 10 « (7)* X² (1) = (3) ₁ + d) 1 t+ 2 10 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
] 1²³ + 0₂ (
X +
N
If x = C₁
3
-2
-2t
=
2
-2
t-1
3
1
a) x² =
**0-(1)+ + + (17)*-(31₂)
t
10
3/2
b) x² =
xo-(3) + (7)*-(32₂)
1
10
2
1
2
< x²()-1(1)^-(31₂)
c) (t)=
=
10
3/2
3
1
d) x² (t) =
²(t) = ( 2 ) ² + (7)**
10
1
is the complementary solution of the nonhomogeneous system
then the particular solution of the system is
3
Transcribed Image Text:] 1²³ + 0₂ ( X + N If x = C₁ 3 -2 -2t = 2 -2 t-1 3 1 a) x² = **0-(1)+ + + (17)*-(31₂) t 10 3/2 b) x² = xo-(3) + (7)*-(32₂) 1 10 2 1 2 < x²()-1(1)^-(31₂) c) (t)= = 10 3/2 3 1 d) x² (t) = ²(t) = ( 2 ) ² + (7)** 10 1 is the complementary solution of the nonhomogeneous system then the particular solution of the system is 3
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