Consider the nonhomogeneous equation x"(t) + ax'(t) + bx(1) = (t). If At) is a constant, say c, then find a solution of this equation under the conditions (i) if b ± 0 (ii) if b = 0 and a ± 0 (iii) if a = b = 0. (CLO-1, PLO-2)

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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Q1. a) Consider the nonhomogeneous equation x"(1) + ax'(t) + bx(t) =At). If flt) is a
constant, say c, then find a solution of this equation under the conditions
(i) if b +0 (ii) if b= 0 and a + 0 (iii) if a = b = 0.
(CLO-1, PLO-2)
b) Also find the solution to above equation given in part when At) = 2sin t + cos t.
(CLO-1, PLO-2)
1 0
Q2. a) Suppose A = 0
1
0 and b(t) =
then find the solutions of the given
7 -3
sin t
dX
= AX and (ii)
dt
dX
= AX + b(t).
dt
system of equations (i)
(CLO-1, PLO-2)
Transcribed Image Text:Q1. a) Consider the nonhomogeneous equation x"(1) + ax'(t) + bx(t) =At). If flt) is a constant, say c, then find a solution of this equation under the conditions (i) if b +0 (ii) if b= 0 and a + 0 (iii) if a = b = 0. (CLO-1, PLO-2) b) Also find the solution to above equation given in part when At) = 2sin t + cos t. (CLO-1, PLO-2) 1 0 Q2. a) Suppose A = 0 1 0 and b(t) = then find the solutions of the given 7 -3 sin t dX = AX and (ii) dt dX = AX + b(t). dt system of equations (i) (CLO-1, PLO-2)
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