Second order homogeneous differential equation

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Matthew Jenkins
Matthew Jenkins 2011-1-20
移动：John D'Errico 2024-10-2
I am trying to figure out how to use MATLAB to solve second order homogeneous differential equation.
A0d2y/dt2 + A1dy/dt + A2y = 0
Here are a couple examples of problems I want to learn how to do.
d2y/dt2 - dy/dt -6y = 0
r1 = 3
r2 = -2
y = C1e3t + C2e-2t (general solution)
d2y/dt2 - 4dy/dt -21y = 0
where:
dy/dt = 0
and
y = 2 when t = 0.
y = 0.6*e^7*t + 1.4*e^-3*t (particular solution)
  2 个评论
Elaina
Elaina 2024-10-2
移动：John D'Errico 2024-10-2
Apparently the ability to use 'Dy' in a string is being removed.... Does anyone know how to do it now?
Torsten
Torsten 2024-10-2
移动：John D'Errico 2024-10-2
Ran in:
Apparently the ability to use 'Dy' in a string is being removed...
No.
dsolve('D2y - Dy - 6*y = 0')
Warning: Support for character vector or string inputs will be removed in a future release. Instead, use syms to declare variables and replace inputs such as dsolve('Dy = -3*y') with syms y(t); dsolve(diff(y,t) == -3*y).
But you should use
syms t y(t)
ode = diff(y,t,2)-diff(y,t)-6*y==0;
dsolve(ode)

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回答（3 个）

Anish
Anish 2011-1-20
You can use the DSOLVE command in the Symbolic Math Toolbox:
>> dsolve('D2y - Dy - 6*y = 0')
ans =
C4*exp(3*t) + C5/exp(2*t)
Alternately, you can use the MuPAD interface in MATLAB (by executing "mupad" at the MATLAB Command Line) and use the "ode::solve" function there.
Note that you would need a license to the Symbolic Math Toolbox to be able to use this functionality.
For more help see:
http://www.mathworks.com/help/toolbox/symbolic/dsolve.html
http://www.mathworks.com/help/toolbox/mupad/ode/solve.html
If you want to solve these ODE's numerically, you can use the ODE suite in MATLAB. For more help, see:
http://www.mathworks.com/support/tech-notes/1500/1510.html
mariam eltohamy
mariam eltohamy 2018-12-7
use this code Untitled.png
mariam eltohamy
mariam eltohamy 2018-12-7
cont.
Untitled2.png

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