Second order homogeneous differential equation

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)

Answer 1

[Anish]

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

Answer 2

[mariam eltohamy]

use this code

Answer 3

[mariam eltohamy]

cont.

Answer 4

[Gabriel]

y^3-2*y^2+3*y=exp^3*x/2*cos^2(sqrt(3)/4*x