EXERCICE  1

solve(x^3+x-4=0,x);

EXERCICE  2

wxplot2d([(4*x-2)*log(2*x-1)+6*x],[x,-1/2+0.0000001,5]);

f(x):=(4*x-2)*log(2*x-1)+6*x;

limit(f(x),x,1/2);

df:factor(diff(f(x),x));

solve(%,x);

limit(df,x,1/2);

diff(df,x);

EXERCICE  3

ode2('diff(y,x,3)-2*'diff(y,x,2)-'diff(y,x)+2*y=0,y,x);

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

eigenvectors(A);

P:matrix([1,1,1],[2,-1,1],[4,1,1]);

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

Z:invert(P).[1,3,-1];

ode2('diff(z1,x)=2*z1,z1,x);

ic1(%,z1=-2/3,x=0);

ode2('diff(z2,x)=-z2,z2,x);

ic1(%,z2=-4/3,x=0);

ode2('diff(z3,x)=z3,z3,x);

ic1(%,z3=3,x=0);

u:P.[-(2*%e^(2*x))/3,-(4*%e^(-x))/3,3*%e^x];

wxplot2d([-(2*%e^(2*x))/3+3*%e^x-(4*%e^(-x))/3],[x,0,2]);