EDO_a:=diff(y(t),t$2)-4*diff(y(t),t)+3*y(t)=(2*t+1)*sinh(t);

NiM+SSZFRE9fYUc2Ii8sKC1JJWRpZmZHSSpwcm90ZWN0ZWRHRio2JC1JInlHRiU2I0kidEdGJS1JIiRHRio2JEYvIiIjIiIiLUYpNiRGLEYvISIlRiwiIiQqJiwmRi9GM0Y0RjRGNC1JJXNpbmhHNiRGKkkoX3N5c2xpYkdGJUYuRjQ=

EDO_b:=2*diff(y(t),t$2)+I*diff(y(t),t)+y(t)=sin(t)+i*cosh(t);

NiM+SSZFRE9fYkc2Ii8sKC1JJWRpZmZHSSpwcm90ZWN0ZWRHRio2JC1JInlHRiU2I0kidEdGJS1JIiRHRio2JEYvIiIjRjMqJl4jIiIiRjYtRik2JEYsRi9GNkY2RixGNiwmLUkkc2luRzYkRipJKF9zeXNsaWJHRiVGLkY2KiZJImlHRiVGNi1JJWNvc2hHRjxGLkY2RjY=

y_a:=dsolve(EDO_a,y(t));

NiM+SSR5X2FHNiIvLUkieUdGJTYjSSJ0R0YlLCgqJi1JJGV4cEc2JEkqcHJvdGVjdGVkR0YwSShfc3lzbGliR0YlRikiIiJJJF9DMkdGJUYyRjIqJi1GLjYjLCRGKiIiJEYySSRfQzFHRiVGMkYyKiZGLUYyLCYqJiwoKiYsJkYyRjJGKkYyRjItSSVjb3NoR0YvNiMsJEYqIiIjRjJGMiomLCZGKiEiIkZHRjJGMi1JJXNpbmhHRi9GQkYyRjIqJiwmRipGMiNGOCIiJUYyRjIsJi1GSTYjLCRGKkZNRjItRkFGUEZHRjIjRjJGREYyLUYuRkJGMkYyKiZGP0YyLChGKkYyRkhGR0ZARjJGMkYyRjIjRkdGTQ==

y_b:=dsolve(EDO_b,y(t));

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

#Cherchons les solutions particuli\350res une \340 une: Th\351or\350me de SuperpositionEDO_a1:=diff(y(t),t$2)-4*diff(y(t),t)+3*y(t)=(2*t+1)*exp(t)/2;

NiM+SSdFRE9fYTFHNiIvLCgtSSVkaWZmR0kqcHJvdGVjdGVkR0YqNiQtSSJ5R0YlNiNJInRHRiUtSSIkR0YqNiRGLyIiIyIiIi1GKTYkRixGLyEiJUYsIiIkLCQqJiwmRi9GM0Y0RjRGNC1JJGV4cEc2JEYqSShfc3lzbGliR0YlRi5GNCNGNEYz

EDO_a2:=diff(y(t),t$2)-4*diff(y(t),t)+3*y(t)=(2*t+1)*exp(-t)/2;

NiM+SSdFRE9fYTJHNiIvLCgtSSVkaWZmR0kqcHJvdGVjdGVkR0YqNiQtSSJ5R0YlNiNJInRHRiUtSSIkR0YqNiRGLyIiIyIiIi1GKTYkRixGLyEiJUYsIiIkLCQqJiwmRi9GM0Y0RjRGNC1JJGV4cEc2JEYqSShfc3lzbGliR0YlNiMsJEYvISIiRjQjRjRGMw==

dsolve(EDO_a1,y(t));dsolve(EDO_a2,y(t));

NiMvLUkieUc2IjYjSSJ0R0YmLCgqJi1JJGV4cEc2JEkqcHJvdGVjdGVkR0YuSShfc3lzbGliR0YmRiciIiJJJF9DMkdGJkYwRjAqJi1GLDYjLCRGKCIiJEYwSSRfQzFHRiZGMEYwKihGKEYwLCYiIiNGMEYoRjBGMEYrRjAjISIiIiIlNiMvLUkieUc2IjYjSSJ0R0YmLCgqJi1JJGV4cEc2JEkqcHJvdGVjdGVkR0YuSShfc3lzbGliR0YmRiciIiJJJF9DMkdGJkYwRjAqJi1GLDYjLCRGKCIiJEYwSSRfQzFHRiZGMEYwKiYsJiIiJkYwRigiIiVGMC1GLDYjLCRGKCEiIkYwI0YwIiNL

EDO_b1:=2*diff(y(t),t$2)+I*diff(y(t),t)+y(t)=exp(t)/2;

NiM+SSdFRE9fYjFHNiIvLCgtSSVkaWZmR0kqcHJvdGVjdGVkR0YqNiQtSSJ5R0YlNiNJInRHRiUtSSIkR0YqNiRGLyIiI0YzKiZeIyIiIkY2LUYpNiRGLEYvRjZGNkYsRjYsJC1JJGV4cEc2JEYqSShfc3lzbGliR0YlRi4jRjZGMw==

EDO_b2:=2*diff(y(t),t$2)+I*diff(y(t),t)+y(t)=exp(-t)/2;

NiM+SSdFRE9fYjJHNiIvLCgtSSVkaWZmR0kqcHJvdGVjdGVkR0YqNiQtSSJ5R0YlNiNJInRHRiUtSSIkR0YqNiRGLyIiI0YzKiZeIyIiIkY2LUYpNiRGLEYvRjZGNkYsRjYsJC1JJGV4cEc2JEYqSShfc3lzbGliR0YlNiMsJEYvISIiI0Y2RjM=

EDO_b1:=2*diff(y(t),t$2)+I*diff(y(t),t)+y(t)=exp(t)/2;

NiM+SSdFRE9fYjFHNiIvLCgtSSVkaWZmR0kqcHJvdGVjdGVkR0YqNiQtSSJ5R0YlNiNJInRHRiUtSSIkR0YqNiRGLyIiI0YzKiZeIyIiIkY2LUYpNiRGLEYvRjZGNkYsRjYsJC1JJGV4cEc2JEYqSShfc3lzbGliR0YlRi4jRjZGMw==

EDO_b3:=2*diff(y(t),t$2)+I*diff(y(t),t)+y(t)=exp(I*t)/(2*I);

NiM+SSdFRE9fYjNHNiIvLCgtSSVkaWZmR0kqcHJvdGVjdGVkR0YqNiQtSSJ5R0YlNiNJInRHRiUtSSIkR0YqNiRGLyIiI0YzKiZeIyIiIkY2LUYpNiRGLEYvRjZGNkYsRjYqJl4jIyEiIkYzRjYtSSRleHBHNiRGKkkoX3N5c2xpYkdGJTYjKiZGNUY2Ri9GNkY2

EDO_b4:=2*diff(y(t),t$2)+I*diff(y(t),t)+y(t)=-exp(-I*t)/(2*I);

NiM+SSdFRE9fYjRHNiIvLCgtSSVkaWZmR0kqcHJvdGVjdGVkR0YqNiQtSSJ5R0YlNiNJInRHRiUtSSIkR0YqNiRGLyIiI0YzKiZeIyIiIkY2LUYpNiRGLEYvRjZGNkYsRjYqJl4jI0Y2RjNGNi1JJGV4cEc2JEYqSShfc3lzbGliR0YlNiMqJl4jISIiRjZGL0Y2RjY=

dsolve(EDO_b1,y(t));dsolve(EDO_b2,y(t));dsolve(EDO_b3,y(t));dsolve(EDO_b4,y(t));

NiMvLUkieUc2IjYjSSJ0R0YmLCgqJi1JJGV4cEc2JEkqcHJvdGVjdGVkR0YuSShfc3lzbGliR0YmNiMqJl4jIyIiIiIiI0Y0RihGNEY0SSRfQzJHRiZGNEY0KiYtRiw2IyomXiMhIiJGNEYoRjRGNEkkX0MxR0YmRjRGNComXiQjIiIkIiM/I0Y8RkJGNC1GLEYnRjRGNA==NiMvLUkieUc2IjYjSSJ0R0YmLCgqJi1JJGV4cEc2JEkqcHJvdGVjdGVkR0YuSShfc3lzbGliR0YmNiMqJl4jIyIiIiIiI0Y0RihGNEY0SSRfQzJHRiZGNEY0KiYtRiw2IyomXiMhIiJGNEYoRjRGNEkkX0MxR0YmRjRGNComXiQjIiIkIiM/I0Y0RkJGNC1GLDYjLCRGKEY8RjRGNA==NiMvLUkieUc2IjYjSSJ0R0YmLCgqJi1JJGV4cEc2JEkqcHJvdGVjdGVkR0YuSShfc3lzbGliR0YmNiMqJl4jIyIiIiIiI0Y0RihGNEY0SSRfQzJHRiZGNEY0KiYtRiw2IyomXiMhIiJGNEYoRjRGNEkkX0MxR0YmRjRGNComXiMjRjQiIiVGNC1GLDYjKiZeI0Y0RjRGKEY0RjRGNA==NiMvLUkieUc2IjYjSSJ0R0YmLCgqJi1JJGV4cEc2JEkqcHJvdGVjdGVkR0YuSShfc3lzbGliR0YmNiMqJl4jIyIiIiIiI0Y0RihGNEY0SSRfQzJHRiZGNEY0KiYtRiw2IyomXiMhIiJGNEYoRjRGNEkkX0MxR0YmRjRGNComRihGNEY4RjQjRjwiIic=