- 
Solve :
Input (typing twice prime for y’’): 
desolve(y’’+y=cos(x),y) or input :desolve((diff(diff(y))+y)=(cos(x)),y) Output :c_0*cos(x)+(x+2*c_1)*sin(x)/2 c_0, c_1 are the constants of integration : y(0)=c_0 and 
y’(0)=c_1.
 If the variable is not x but t, input :
desolve(derive(derive(y(t),t),t)+y(t)=cos(t),t,y)
 Output :c_0*cos(t)+(t+2*c_1)/2*sin(t) c_0, c_1 are the constants of integration : y(0)=c_0 and
y’(0)=c_1.
- Solve :
Input :
desolve([y’’+y=cos(x),y(0)=1],y) Output :[cos(x)+(x+2*c_1)/2*sin(x)] the components of this vector are solutions (here there is just one component, 
so we have just one solution depending of the constant c_1).
- Solve :
Input :
desolve([y’’+y=cos(x),y(0)^2=1],y)
 Output :[-cos(x)+(x+2*c_1)/2*sin(x),cos(x)+(x+2*c_1)/2*sin(x)] each component of this list is a solution, 
we have two solutions depending
on the constant c_1 (y′(0)=c1)
and corresponding to y(0)=1 and to y(0)=−1.
- Solve :
| y″+y=cos(x),     (y(0))2=1     y′(0)=1 |  
 Input :desolve([y’’+y=cos(x),y(0)^2=1,y’(0)=1],y)
 Output :[-cos(x)+(x+2)/2*sin(x),cos(x)+(x+2)/2*sin(x)] each component of this list is a solutions (we have two solutions).
- Solve :
Input :
desolve(y’’+2*y’+y=0,y) Output :(x*c_0+x*c_1+c_0)*exp(-x) the solution depends of 2 constants of integration : 
c_0, c_1 (y(0)=c_0 and y’(0)=c_1).
- Solve :
Input:
desolve(y’’-6*y’+9*y=(x*exp(3*x),y) Output :(x^3+(-(18*x))*c_0+6*x*c_1+6*c_0)*1/6*exp(3*x)
 the solution depends on 2 constants of integration : 
c_0, c_1 (y(0)=c_0 and y’(0)=c_1).