Example 1: Solve .

Notice that the right hand side can be simplified. We can use Maple command simplify to faciliate out calculations.

> simplify(exp(y)*x/(exp(y)+x^2*exp(y)));

Thus the equation is equivalent to which can be easily separated as

and now we integrate the both sides using Maple command int as follows

> int(1,y)=int(x/(1+x^2),x)t color=#FF0000>int(1,y)=int(x/(1+x^2),x)+C;

To check that this is indeed a solution we simply differentiate the right hand side using Maple command diff and compare the result with . First we have to make a function of . We do this using Maple command unapply as follows:

> y:=unapply(1/2*ln(1+x^2)+C,x);

> diff(y(x),x);