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y"- y'=0 ; y, (t) =e y,(1)=e* y= 3t +r a. b. y"+2y'-3y 0 c. ty'-y=r ; y. (1) = cosht y:(1)=d : с.

y"- y'=0 ; y, (t) =e y,(1)=e* y= 3t +r a. b. y"+2y'-3y 0 c. ty'-y=r ; y. (1) = cosht y:(1)=d : с.

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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Part I Verify that each given function is a solution of the differential equation. y. (1)=e' y (1) =e y = 3t +r y, (1)=cosht y: (1)=e a. y"-y'=0 ; b. y"+2y'-3y= 0 c. ーy=r: d. y""+ 4y"+3y=t (1)=c" + e. 21 y"+3ty'-y=0, t>0 f. ty"+5ty'+ 4y 0, t>0 : 0<t< n/2 y (1) =r y, (1)=rInt y=(cost)Incost + t sint , (1)=r g. y"+ y = sect, h. y'-2ty 1, t>0 y(1) =e" ['e*ds+e i. y'=- *+y = 25 : j. 2y'+ y = 0 ; y=e2 6 6 y ==--e 5 5 dy k. + 20y = 24 dt 1. y"-6y'+13y=0 m. (y-x)y'=y-x+8 ; n. y'= 25+ y o. 2y'= y' cos x y = e" cos 2x y = x+4x+2 y =5 tan 5x -1/2 y=(1-sin.x)2
Transcribed Image Text:Part I Verify that each given function is a solution of the differential equation. y. (1)=e' y (1) =e y = 3t +r y, (1)=cosht y: (1)=e a. y"-y'=0 ; b. y"+2y'-3y= 0 c. ーy=r: d. y""+ 4y"+3y=t (1)=c" + e. 21 y"+3ty'-y=0, t>0 f. ty"+5ty'+ 4y 0, t>0 : 0<t< n/2 y (1) =r y, (1)=rInt y=(cost)Incost + t sint , (1)=r g. y"+ y = sect, h. y'-2ty 1, t>0 y(1) =e" ['e*ds+e i. y'=- *+y = 25 : j. 2y'+ y = 0 ; y=e2 6 6 y ==--e 5 5 dy k. + 20y = 24 dt 1. y"-6y'+13y=0 m. (y-x)y'=y-x+8 ; n. y'= 25+ y o. 2y'= y' cos x y = e" cos 2x y = x+4x+2 y =5 tan 5x -1/2 y=(1-sin.x)2
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