x"(t) + 2x(t) − y'(t) = 2t +5 x' (t) − x(t) + y' (t) + y(t) = −2t −1 when : x(0) = 3, x'(0) = 0, y(0) = −3 x(t) = 2+t+e=²¹ Ans. y(t) =1−t−3e¯²¹ − cost
x"(t) + 2x(t) − y'(t) = 2t +5 x' (t) − x(t) + y' (t) + y(t) = −2t −1 when : x(0) = 3, x'(0) = 0, y(0) = −3 x(t) = 2+t+e=²¹ Ans. y(t) =1−t−3e¯²¹ − cost
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Topic: Systems of Linear
Please show me how to solve these two questions. Take note of the topic as it will be the method used.
Transcribed Image Text:1. _x"(t)+2x(t) − y' (t) = 2t + 5
x' (t) − x(t) + y' (t) + y(t) = −2t −1
when: x(0) = 3, x'(0) = 0, y(0) = −3
Ans. x(t)=2+t+e²²¹
y(t) =1-t-3e-²¹ - cost
Transcribed Image Text:2._x"(t)+3y'(t) + 3y(t) = 0
x"(t)
+3y(t)=te¯¹
x(0)=0, x'(0) = 2, y(0)=0
1
Ans. x(t) == t² +t+1-e²
2
y(t) =
1
3
+
1
3
e
+
1
-
3
tet
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VIEWStep 2: Re- write the given system using the usual operator D=d/dt
VIEWStep 3: Determine the complementary function
VIEWStep 4: Determine the particular integral
VIEWStep 5: Determine y(t) using the determined x(t) and the given equations
VIEWStep 6: Apply the given conditions to find x(t) and y(t)
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