restart;EDO:=m*diff(x(t),t$2)=-a*x(t);

NiM+SSRFRE9HNiIvKiZJIm1HRiUiIiItSSVkaWZmR0kqcHJvdGVjdGVkR0YsNiQtSSJ4R0YlNiNJInRHRiUtSSIkR0YsNiRGMSIiI0YpLCQqJkkiYUdGJUYpRi5GKSEiIg==

assume(m,positive);assume(a,positive);sol_stab:=rhs(dsolve({EDO,x(0)=x_0,D(x)(0)=0},x(t)));

NiM+SSlzb2xfc3RhYkc2IiomSSR4XzBHRiUiIiItSSRjb3NHNiRJKnByb3RlY3RlZEdGLEkoX3N5c2xpYkdGJTYjKigqJkkjYXxpckdGJUYoSSNtfGlyR0YlRigjRigiIiNGMiEiIkkidEdGJUYoRig=

assume(a<0);sol_instab:=rhs(dsolve({EDO,x(0)=x_0,D(x)(0)=0},x(t)));

NiM+SStzb2xfaW5zdGFiRzYiLCYqJkkkeF8wR0YlIiIiLUkkZXhwRzYkSSpwcm90ZWN0ZWRHRi1JKF9zeXNsaWJHRiU2IyooLCQqJkkjYXxpckdGJUYpSSNtfGlyR0YlRikhIiIjRikiIiNGNEY1SSJ0R0YlRilGKUY2KiZGKEYpLUYrNiMsJEYwRjVGKUY2

#Remarquez que la solution n'est rien d'autre que la transcription de la solution stable en remplacant cos par ch.assume(a=0);sol_indif:=rhs(dsolve({EDO,x(0)=x_0,D(x)(0)=0},x(t)));

NiM+SSpzb2xfaW5kaWZHNiJJJHhfMEdGJQ==

#Tracons les courbes associ\351esm:=1;x_0:=1;

NiM+SSJtRzYiIiIiNiM+SSR4XzBHNiIiIiI=

a:=1;y_stab:=rhs(dsolve({EDO,x(0)=x_0,D(x)(0)=0},x(t)));

NiM+SSJhRzYiIiIiNiM+SSd5X3N0YWJHNiItSSRjb3NHNiRJKnByb3RlY3RlZEdGKUkoX3N5c2xpYkdGJTYjSSJ0R0Yl

a:=-0.1;y_instab:=rhs(dsolve({EDO,x(0)=x_0,D(x)(0)=0},x(t)));

NiM+SSJhRzYiJCEiIkYnNiM+SSl5X2luc3RhYkc2IiwmLUkkZXhwRzYkSSpwcm90ZWN0ZWRHRipJKF9zeXNsaWJHRiU2IywkKiYiIzUjIiIiIiIjSSJ0R0YlRjEjRjFGL0YwLUYoNiMsJEYuIyEiIkYvRjA=

a:=0;y_indif:=rhs(dsolve({EDO,x(0)=x_0,D(x)(0)=0},x(t)));

NiM+SSJhRzYiIiIhNiM+SSh5X2luZGlmRzYiIiIi

plot([y_stab,y_instab,y_indif],t=0..10,color=[red,black,blue]);

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