Hello everyone,

I am trying to solve a system of ODE's numerically but the problem is with the condition f(0)+g(0)=1.

Here is the system with the initial conditions,

restart:
ode1:=diff(f(x), x,x)+(f(x)+g(x))*diff(f(x),x)=0;
ode2:=diff(g(x), x,x)+(f(x)+g(x))*diff(g(x),x)=0;
ics:=f(0)+g(0)=1,D(f)(0) =0,D(g)(0) =1;
dsolve({ode1,ode2,ics},numeric);

which give an error

Error, (in DEtools/convertsys) invalid specification of initial conditions

The above system is a simplified form of a very complicated one.

I am having trouble to display a 3d and a 2d plots in a same figure. I tried with the display command but no luck.

f1:=exp(x*y);

plot3d(f1,x=0..1,y=0..1);

p1:=%:

f2:=exp(x);

plot(f2,x=0..1);

p2:=%:

To combine both I used display

display(p1,p2);

I ends up with a structure error

The second question is how to plot f(x,y,z)=exp(x+y+z)?

Thanks

Is it possible to do the ab-initio method for differentiation in maple?

I am trying to find a general solution to the 1D-wave equation

Eq1:=diff(u(x,t),t$2)=diff(u(x,t),x$2);

pdsolve(Eq1,HINT=f(x)*g(t)); # Hinting pdsolve gives general solution using separation of variables

pdsolve({Eq1,u(x,0)=f(x),D[2](u)(x,0)=g(x)}); # without HINT and using intial conditions, I get travelling wave solution

pdsolve({Eq1,u(x,0)=f(x),D[2](u)(x,0)=g(x)},HINT=f(x)*g(t)); # Now when I try to use hint and ICs both, pdsolve return nothing.

I want to use separation of variables to find solution to the wave equation.

Any comment?

Thanks

restart:

f:=exp(-I*Im(s)*(t)); # I is iota, s is a complex number and t is time.

simplify(%);

Thanks