ODE Inverse Laplace Transformation Constants Error

Hey guys! I'm trying to use matlab to solve an ODE with the following IC's: y(0) = 2, y'(0) = 0 and the function u(t) = 3*exp(-2*t). The ODE is 3*y''+12*y'+9*y = 9*u'+14*u(t). The code I used in matlab is as follows:

clear; clc; close all;

syms u(t) y(t) s

Dy = diff(y);

u(t) = 3*exp(-2*t)

ode1 = 3*diff(diff(y))+12*diff(y)+9*y == 9*diff(u)+14*u

cond1 = y(0) == 2;

cond2 = Dy(0) == 0;

conds = [cond1 cond2]

ySol1 = dsolve(ode1, conds)

The function that is returned is exp(-3*t)*(exp(2*t)+4*exp(t)-3) when it should be returning (11/2)*exp(-t)+4*exp(-2*t)-(15/2)*exp(-3*t). The constants for the partital fraction decomposition seem to be wrong. What could the issue be with my code? I'm using it to double check my handwork for a dyanmic systems modeling class. Thanks in advance for any help!

[Rik]

Question originally posted by Ri Eld (restored from Google cache):

ODE Inverse Laplace Transformation Constants Error

Hey guys! I'm trying to use matlab to solve an ODE with the following IC's: y(0) = 2, y'(0) = 0 and the function u(t) = 3*exp(-2*t). The ODE is 3*y''+12*y'+9*y = 9*u'+14*u(t). The code I used in matlab is as follows:

clear; clc; close all;
syms u(t) y(t) s  
Dy = diff(y);
u(t) = 3*exp(-2*t)
ode1 = 3*diff(diff(y))+12*diff(y)+9*y == 9*diff(u)+14*u
cond1 = y(0) == 2;
cond2 = Dy(0) == 0;
conds = [cond1 cond2]
ySol1 = dsolve(ode1, conds)

The function that is returned is exp(-3*t)*(exp(2*t)+4*exp(t)-3) when it should be returning (11/2)*exp(-t)+4*exp(-2*t)-(15/2)*exp(-3*t). The constants for the partital fraction decomposition seem to be wrong. What could the issue be with my code? I'm using it to double check my handwork for a dyanmic systems modeling class. Thanks in advance for any help!

[Rena Berman]

(Answers Dev) Restored edit

Answer 1

[Alan Stevens]

The solution you think is correct does not satisfy the condition y`(0) = 0. It gives y`(0) = 9.

MATLAB's solution satisfies both initial conditions.