Example 2: Solve .

Solution: First we multiply both sides with to obtain . Divide both sides of the equation with to obtain . Finally rewrite this as . Since we have separated variables we integrate both sides.

> int(1/y,y)=int(x*exp(x)+2,x);

We can solve this explicitly in .

> solve(ln(y) = x*exp(x)-exp(x)+2*x,y);

To check that this is indeed a solution we first make it as a function of using Maple command unapply together with % , which in Maple denotes Maple expression that was last executed.

> y:=unapply(%,x);

We will plug this back in the original equation, and using Maple command simplify we should get as the answer.

> simplify(D(y)(x)-y(x)-y(x)*(x*exp(x)+1));