## DIFFERENTIAL EQUATION SYSTEM

Help
momo
2011-08-28
2012-11-20

• momo
2011-08-28

Hello
There is a function(or packages) in REDUCE the a differential equation system is converted to a linear DES?
In other words a function to solve a non-linear or homogene differential equation(no odesolve)
for example how to solve the differential equation system
DF(x,u) = y + sin(u)
DF(y,_u) = z
DF(z,_u) =-y+cos(u)

Thank you

• Francis Wright
2011-08-30

Take a look at the CRACK package, which is distributed with REDUCE.

Francis

• thomasjwolf
2011-08-30

Should _u in the 2. and 3. equation be u?
If x=x(u), y=y(u), z=z(u) then the system is already linear in x,y,z. This actually is a system of 2 equations (2. and 3.) for 2 functions y,z and if they are solved the x is computed from the first equation. To solve the 2. and 3. equation I would
substitute z from the 2. into the 3. giving a 2nd order ODE with sin(u), cos(u) solutions of the homogeneous part and then make coefficients u-dependent,, substitute and compute them to solve the inhomogeneous 2nd order ODE.

Thomas

• momo
2011-08-31

Hello,
Thanks for your help.
I'm going to look like it works with crack.
Thank you