/usr/share/maxima/5.32.1/demo/eaton1.dem is in maxima 5.32.1-1.
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1 2 3 4 5 6 7 8 9 10 11 12 | /* solution of simultaneous differential equations */
eq1:3*'diff(f(x),x,2)-2*'diff(g(x),x)=sin(x);
eq2:a*'diff(g(x),x,2)+'diff(f(x),x)=a*cos(x);
atvalue(g(x),x=0,1)$
atvalue('diff(f(x),x),x=0,0)$
atvalue('diff(g(x),x),x=0,1)$
laplace_eq1:laplace(eq1,x,s);
laplace_eq2:laplace(eq2,x,s);
solve([laplace_eq1,laplace_eq2],
['laplace(f(x),x,s),'laplace(g(x),x,s)]);
ilt(%,s,x);
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