ODE Inverse Laplace Transformation Constants Error
3 visualizaciones (últimos 30 días)
Mostrar comentarios más antiguos
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!
2 comentarios
Rik
el 2 de Nov. de 2020
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!
Respuestas (1)
Alan Stevens
el 10 de Ag. de 2020
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.
0 comentarios
Ver también
Categorías
Más información sobre Equation Solving en Help Center y File Exchange.
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!