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Differential Equations - Symbolic Solutions

Continuation


To solve the equation of the previous example with the function desolve, we introduce names for the two equations:

diff_eq1: 'diff(f(x),x,2) + 'diff(g(x),x) + 3*f(x) = 15*exp(-x);
			       2
		  d	      d				 - x
(%o1) 		  -- (g(x)) + --- (f(x)) + 3 f(x) = 15 %e
		  dx	        2
			      dx
diff_eq2: 'diff(g(x), x, 2) - 4*'diff(f(x), x) + 3*g(x) = 15*sin(2*x);
		2
	       d	       d
(%o2) 	       --- (g(x)) - 4 (-- (f(x))) + 3 g(x) = 15 sin(2 x)
		 2	       dx
	       dx

Now we form a named system of equations:

ode_syst: [diff_eq1, diff_eq2];
		    2
       d	   d			      - x
(%o3) [-- (g(x)) + --- (f(x)) + 3 f(x) = 15 %e	 , 
       dx	     2
		   dx

			      2
			     d		     d
			     --- (g(x)) - 4 (-- (f(x))) + 3 g(x) = 15 sin(2 x)]
			       2	     dx
			     dx

The initial values are specified in the same manner as in the previous example:

atvalue (f(x), x=0, 35);
      35
atvalue ('diff(f(x),x),x=0, -48);
     - 48
atvalue (g(x), x=0, 27);
      27
atvalue ('diff(g(x), x), x=0, -55);
     - 55

Now we call desolve:

desolve(ode_syst, [f(x), g(x)]);

and obtain a list of two equations, the solution of the given system.

							   - x
(%o8) [f(x) = - 15 sin(3 x) + 2 cos(2 x) + 30 cos(x) + 3 %e   , 

									   - x
			   g(x) = 30 cos(3 x) + sin(2 x) - 60 sin(x) - 3 %e   ]


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