simplify(exp(x^2)*(C+(1+x^2)*exp(-x^2)));

It seems the result is not the simplest?

dsolve(diff(y(x), x)-x*y(x)+exp(-y(x)))

It's strange that no information come out.

And no such form to solve a DE such as not a DE?

dsolve(diff(y(x), x) = x*y(x)-exp(-y(x)), y(x))

it looks like this in Maple:dsolve(y'=x*y-exp(-y),y)

f(z):=x^(n)+I y^(n);

diff(f(z), x)=

x^n*n/x

simplify(x^n*n/x)=x^(n-1)*n

plot(e^x*tan(x), x = 0 .. 1)

plot(evalf(e^x*tan(x)), x = 0 .. 1)

question2:

sin(0)=0, why this is not sin(0)?

sin(1)=sin(1)?