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(b) Find the solution of the following initial value problem y" – 4y" – 5y' = 9+ 5z, y(0) = 0, y' = 0 and y"(0) = 4 The general solution is y Yn + Yp (The notation and symbols as used in the lecture notes) YA = C1 + cz exp( )+cz exp(5z), where c1, cz and cz are arbitrary constants The nonhomogeneous solution can be represented in the form Yp = Ap(z) + Bq(z) +Cr(z): where P(z), q(z) and r(z) are polynomial of degree n > 0. Find the values of the arbitrary constants A, B,C. A= .c- { Express your answer in decimal where applicable} Using initial conditions, find the corresponding values of the arbitrary constants C1, C2 and c3 . C1 = { Express your answer in decimal where applicable }. Thus the particular solution of the ordinary differential equation is given by y =(exp( +1))

(b) Find the solution of the following initial value problem y" – 4y" – 5y' = 9+ 5z, y(0) = 0, y' = 0 and y"(0) = 4 The general solution is y Yn + Yp (The notation and symbols as used in the lecture notes) YA = C1 + cz exp( )+cz exp(5z), where c1, cz and cz are arbitrary constants The nonhomogeneous solution can be represented in the form Yp = Ap(z) + Bq(z) +Cr(z): where P(z), q(z) and r(z) are polynomial of degree n > 0. Find the values of the arbitrary constants A, B,C. A= .c- { Express your answer in decimal where applicable} Using initial conditions, find the corresponding values of the arbitrary constants C1, C2 and c3 . C1 = { Express your answer in decimal where applicable }. Thus the particular solution of the ordinary differential equation is given by y =(exp( +1))

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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(b) Find the solution of the following initial value problem y" – 4y" – 5y' = 9+ 5x, y(0) = 0, y' = 0 and y"(0) = 4 Finis Time The general solution is y = Yh + Yp (The notation and symbols as used in the lecture notes) Yh = C1 + c2 exp( )+cz exp(5z), where c1, c2 and cz are arbitrary constants The nonhomogeneous solution can be represented in the form yp Ap(x) + Bq(x) + Cr(x): where p(z), q(z) and r(z) are polynomial of degree n > 0. Find the values of the arbitrary constants A, B, C. A = B = { Express your answer in decimal where applicable} Using initial conditions, find the corresponding values of the arbitrary constants C1, c2 and c3 . Ci = ,c2 = ,c3 = { Express your answer in decimal where applicable }. ON Thus the particular solution of the ordinary differential equation is given by y = (exp( +1)) (c). Consider the non-homogeneous ordinary differential equation y" + 4y = 4t2 + 10e-t (i). Find a fundamental pair of solutions for the associated homogeneous equation. У. (t) — сos( ), y2(t) =, (ii) Find a particular solution of the non-homogeneous equations. Yp = A+ B +Ct + Dexp( (iii) Write out the general solution of the non-homogeneous equation. 1. exp/
Transcribed Image Text:(b) Find the solution of the following initial value problem y" – 4y" – 5y' = 9+ 5x, y(0) = 0, y' = 0 and y"(0) = 4 Finis Time The general solution is y = Yh + Yp (The notation and symbols as used in the lecture notes) Yh = C1 + c2 exp( )+cz exp(5z), where c1, c2 and cz are arbitrary constants The nonhomogeneous solution can be represented in the form yp Ap(x) + Bq(x) + Cr(x): where p(z), q(z) and r(z) are polynomial of degree n > 0. Find the values of the arbitrary constants A, B, C. A = B = { Express your answer in decimal where applicable} Using initial conditions, find the corresponding values of the arbitrary constants C1, c2 and c3 . Ci = ,c2 = ,c3 = { Express your answer in decimal where applicable }. ON Thus the particular solution of the ordinary differential equation is given by y = (exp( +1)) (c). Consider the non-homogeneous ordinary differential equation y" + 4y = 4t2 + 10e-t (i). Find a fundamental pair of solutions for the associated homogeneous equation. У. (t) — сos( ), y2(t) =, (ii) Find a particular solution of the non-homogeneous equations. Yp = A+ B +Ct + Dexp( (iii) Write out the general solution of the non-homogeneous equation. 1. exp/
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