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(c). Consider the non-homogeneous ordinary differential equation y" + dy = 4e + 10e 0. Find a fundamental pair of solutions for the associated homogeneous equation. n(t) – com( () Find a particular solution of the non-homogeneous equations. +C€ + Dexp( (ii) Write out the general solution of the non homogeneous equation. exp

(c). Consider the non-homogeneous ordinary differential equation y" + dy = 4e + 10e 0. Find a fundamental pair of solutions for the associated homogeneous equation. n(t) – com( () Find a particular solution of the non-homogeneous equations. +C€ + Dexp( (ii) Write out the general solution of the non homogeneous equation. exp

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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QUESTION THREE (a). Solve the differential equation y' %3D The general solution is: y? %3D (b) Find the solution af the following initial value problem y" – 4g" – 5g' = 9+ 5z, (0) = 0, y =0 and y"(0) =4 The general solution is y = % + , (The notation and symbols as used in the lecture notes) VA =4tg exp( +e, exp(5z). where c, and e, are arbitrary constants The nonhomageneous solution can be represented in the form y, = Ap(z) + Bg(z) + Cr(z): where p(z), g(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, 2 and a. { Express your answer in decimal where applicable }. Thus the particular salution of the ardinary differential equation is given by y=(exp (c). Consider the non-homogeneous ordinary differential equation y" + 4y = 4f + 10e 0. Find a fundamental pair of solutions for the associated homogeneous equation. V (t) = cos( ), (t) = () Find a particular solution of the non-homogeneous equations. =A+B +Ce + Dexp (iii) Write out the general solution of the non-homogeneous equation. y, = exp( Previous page
Transcribed Image Text:QUESTION THREE (a). Solve the differential equation y' %3D The general solution is: y? %3D (b) Find the solution af the following initial value problem y" – 4g" – 5g' = 9+ 5z, (0) = 0, y =0 and y"(0) =4 The general solution is y = % + , (The notation and symbols as used in the lecture notes) VA =4tg exp( +e, exp(5z). where c, and e, are arbitrary constants The nonhomageneous solution can be represented in the form y, = Ap(z) + Bg(z) + Cr(z): where p(z), g(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, 2 and a. { Express your answer in decimal where applicable }. Thus the particular salution of the ardinary differential equation is given by y=(exp (c). Consider the non-homogeneous ordinary differential equation y" + 4y = 4f + 10e 0. Find a fundamental pair of solutions for the associated homogeneous equation. V (t) = cos( ), (t) = () Find a particular solution of the non-homogeneous equations. =A+B +Ce + Dexp (iii) Write out the general solution of the non-homogeneous equation. y, = exp( Previous page
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