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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
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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Topic: Systems of Linear Differential Equation

 

Please show me how to solve these two questions. Take note of the topic as it will be the method used. 

 

 

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: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
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
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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