axy' + bxy' +cy = 0 characteristic equation is, ar + (6- a)r +e= 0 case I: two different real roots → y=C,x* +C,x* case II : two equal real roots →y-C,x +Cx* Inx case III : two conjugate complex roots → yC, cos(Blnx)+C, sin(Bln x)) 4xy+17y 0 is given. 1- the solution of the given cauch-euler diff.equation is I+y-C,x' +C,x? II →y-C,r" +C,r² Inx II → yC, cos(In x)+C, sin(In x) IV → y"(C, cos(21n x)+C, sin(21n x) V →y*C, cos(2x) +C, sin(2x)) OA) IV OB) I OC) V OD) II OE) II
axy' + bxy' +cy = 0 characteristic equation is, ar + (6- a)r +e= 0 case I: two different real roots → y=C,x* +C,x* case II : two equal real roots →y-C,x +Cx* Inx case III : two conjugate complex roots → yC, cos(Blnx)+C, sin(Bln x)) 4xy+17y 0 is given. 1- the solution of the given cauch-euler diff.equation is I+y-C,x' +C,x? II →y-C,r" +C,r² Inx II → yC, cos(In x)+C, sin(In x) IV → y"(C, cos(21n x)+C, sin(21n x) V →y*C, cos(2x) +C, sin(2x)) OA) IV OB) I OC) V OD) II OE) II
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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Transcribed Image Text:ar'y'+ bxy' +cy = 0→ characteristic equation is,
ar + (6- a)r +e = 0
case I: two different real roots → y=C,x* +C,x*
case II : two equal real roots →y-C,x +C,r* Inx
case III : two conjugate complex roots → y=C, cos(ßlnx)+C, sin(Bln x))
4xy+17y 0 is given.
1-
the solution of the given cauch-euler diff.equation is
I→y-C,x' +C,x?
II →y-C,r" +C,r² Inx
III → yC, cos(In x)+C, sin(In x))
IV →y"(C, cos(21n x)+C, sin(2ln x)
V →yx*C, cos(2x)+C, sin(2x))
OA) IV
OB) I
OC) V
OD) III
OE) II
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