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1. Using Laplace Transform solve initial value problem y"+3y'+2y=e* ; y(0)= y'(0)=0

1. Using Laplace Transform solve initial value problem y"+3y'+2y=e* ; y(0)= y'(0)=0

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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1. Using Laplace Transform solve initial value problem y"+3y'+2y =e" ; y(0)=y'(0)=0 a. b. y'-3y = e*; y(0) = 4. Ans : y(e) = e"(+ + 4) c. y'-2y =e"; y(0) = 4. d. y"+y =t ; y(0) = 0 ; y'(0)=2 e. y"-4y = e" ; y(0)=0 ; y'(0)=0 f. y'+2y = 26sin 31 y(0) = 3 g y'+2y = 4y h. y"+3y'+2y = 6e y+4y = cos 21 ; y(0)=1 ; y'(0)=1 j. y"-2y'+y=e ; y(0)=0 ; y'(0)=0 k. y"+9y = 6 ; y(0)=1 ; y'(0)=0 y"+y'+y =1 y(0) = 3 ; y(0)=1 ; y'(0)= 2 i. ; y(0) = y'(0)= 0 ; y(0)= y'(0)= y"(0)= 0 1. m. y"-4y = e' +t y"+2y'+y = 3te" ; y(0)=4 ; y'(0)= 2 n. y"+16y = 321 ; y(0)= 3 ; y'(0)=-2 O. Ans : y(t) = 2-2e' +e p. y"-3y'+2y = 4 ; y(0)=1; y'(0)=0 4. y"+4y'+4y = 6e ; (0)=-2 ; y'(0)=8 y-3y = 6 :y(0) = -1 Ans : y(t)=e* -2 r. y'+4y +16 = 0 :y(0) = -2 S. y"+4y =t :y(0) = 0 :y (0)= 0 Ans : y(t) =t-sin(21) t. 4 y'+3y = 9 :y(0) = 1 u. 3y'ay= :>(0) = 5 w. y-2y = 41 - e ;(0)= 2 y'+y-2y = 4 ;y(0)= 2 ;y'(0) = 1 Ans : y(e) = -2+ 3e +e X. y. y+y = 4te* ;(0) = 3 2y'+y = 8te +6 :>(0) = -7 Z.
Transcribed Image Text:1. Using Laplace Transform solve initial value problem y"+3y'+2y =e" ; y(0)=y'(0)=0 a. b. y'-3y = e*; y(0) = 4. Ans : y(e) = e"(+ + 4) c. y'-2y =e"; y(0) = 4. d. y"+y =t ; y(0) = 0 ; y'(0)=2 e. y"-4y = e" ; y(0)=0 ; y'(0)=0 f. y'+2y = 26sin 31 y(0) = 3 g y'+2y = 4y h. y"+3y'+2y = 6e y+4y = cos 21 ; y(0)=1 ; y'(0)=1 j. y"-2y'+y=e ; y(0)=0 ; y'(0)=0 k. y"+9y = 6 ; y(0)=1 ; y'(0)=0 y"+y'+y =1 y(0) = 3 ; y(0)=1 ; y'(0)= 2 i. ; y(0) = y'(0)= 0 ; y(0)= y'(0)= y"(0)= 0 1. m. y"-4y = e' +t y"+2y'+y = 3te" ; y(0)=4 ; y'(0)= 2 n. y"+16y = 321 ; y(0)= 3 ; y'(0)=-2 O. Ans : y(t) = 2-2e' +e p. y"-3y'+2y = 4 ; y(0)=1; y'(0)=0 4. y"+4y'+4y = 6e ; (0)=-2 ; y'(0)=8 y-3y = 6 :y(0) = -1 Ans : y(t)=e* -2 r. y'+4y +16 = 0 :y(0) = -2 S. y"+4y =t :y(0) = 0 :y (0)= 0 Ans : y(t) =t-sin(21) t. 4 y'+3y = 9 :y(0) = 1 u. 3y'ay= :>(0) = 5 w. y-2y = 41 - e ;(0)= 2 y'+y-2y = 4 ;y(0)= 2 ;y'(0) = 1 Ans : y(e) = -2+ 3e +e X. y. y+y = 4te* ;(0) = 3 2y'+y = 8te +6 :>(0) = -7 Z.
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