Quelques EDO issues de la feuille de TD de MA300

eq:2*t*(1-t)*'diff(y,t)+(1-2*t)*y-1;

ode2(eq,y,t);

ode2('diff(y,t)+2*t*y,y,t);

ode2(t^3*'diff(y,t)-t^2*y-1,y,t);

ode2('diff(y,t)-(1+t)*y-(1+t),y,t);

ic1(%,t=0,y=y0);

ode2('diff(y,t)-%e^(-t^2)*y,y,t);

a:2$b:1$ode2('diff(y,t,2)+a*'diff(y,t)+b*y,y,t);

assume(n>-2);ode2('diff(y,t,2)-n*'diff(y,t)+y-sin(2*t),y,t);

ode2('diff(y,t,2)+t*y,y,t);

desolve(['diff(x(t),t)-2*y(t)-2*z(t),'diff(y(t),t)+x(t)-2*y(t)-2*z(t),'diff(z(t),t)+x(t)-y(t)-3*z(t)],[x(t),y(t),z(t)]);

A:matrix([0,2,2],[-1,2,2],[-1,1,3]);

eigenvalues(A);

tracé de portrait de phase (pendule non linéaire)

load(plotdf);

plotdf([v,-sin(k*z/m)], [z,v], [parameters,"m=2,k=2"],
                           [sliders,"m=1:5"], [trajectory_at,6,0])$