<h3> > with(DEtools); > # Graphing the directionfield of a DE and solving the DE; > # 1.We define a differential equation as follows > de:=diff(y(x),x)=y/(1+x^2); > # 2.Graphing the direction field > DEplot(de,y(x),x=-2..2,y=-2..2); > # 3. Solving the DE. The " _C1 " stands for multiplication by arbitrary constant C1 > f:=dsolve(de,y(x)); > # 4. Initial value problem > f:=dsolve({de,y(0)=5},y(x)); > # 5. Lets consider an other ODE: > de:=diff(y(x),x)=x+cos(y(x)); > dsolve(de,y(x)); > # No answer because the ODE is too hard. We will use numerical methods (Euler's method)