Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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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
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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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