-t 45+2 +25 +5 4e cas 2t + 4esia 2t

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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Q1: True or False
D L'12) = 4easzt + 4e sinzt
+ ye sinzt
2) the third term in the series selution fer the I.v.P
yıt 2xy'+3/ =o
yk) =-1
is
3)If Y1 and y2 afe two solutiens to the nonhomegenous equation
ay" +by'+cy= fox) , thea their diffesence y1- Ye is a soletion of
the homogeneous equaion ayu,by cY s0
Y) If WCtg) = sint then the functions f,gace linearly t
indepandent
%3D
5If the roots of the indicial equarion nfe -03 , -l1 then the D.E has two
linearly independent sokuions
The lower beund for the paolius of canvergance fes the serier sekution
of xy" + 3xy-y o abcut X=3 is 3
) If a lineas diffeential equation has a seluatn at a foinit then thie
Selution is unique
3 the die y'e
sepataple
the die y. 4xY+5yt
sefarable Auaten.
himigenems ond can be tenstormed ini
1) the genefal solution for *y"+34Y+Y=e, x is
Dメュ-3
is
a R.s.P for k+)"y" zxy+ C1-X)y =0
12) Ues +On) Uay = y is lineas
13) 4he function Ya Inx is aseluhion fer tbe die y Hr . onia
interval Co,ae)
Transcribed Image Text:Q1: True or False D L'12) = 4easzt + 4e sinzt + ye sinzt 2) the third term in the series selution fer the I.v.P yıt 2xy'+3/ =o yk) =-1 is 3)If Y1 and y2 afe two solutiens to the nonhomegenous equation ay" +by'+cy= fox) , thea their diffesence y1- Ye is a soletion of the homogeneous equaion ayu,by cY s0 Y) If WCtg) = sint then the functions f,gace linearly t indepandent %3D 5If the roots of the indicial equarion nfe -03 , -l1 then the D.E has two linearly independent sokuions The lower beund for the paolius of canvergance fes the serier sekution of xy" + 3xy-y o abcut X=3 is 3 ) If a lineas diffeential equation has a seluatn at a foinit then thie Selution is unique 3 the die y'e sepataple the die y. 4xY+5yt sefarable Auaten. himigenems ond can be tenstormed ini 1) the genefal solution for *y"+34Y+Y=e, x is Dメュ-3 is a R.s.P for k+)"y" zxy+ C1-X)y =0 12) Ues +On) Uay = y is lineas 13) 4he function Ya Inx is aseluhion fer tbe die y Hr . onia interval Co,ae)
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