Thanks. But I think square brackets are good in my Maple. Anyway I don't even know how to integrate it. The problem is that (I think), that I can't refer to sol as a function.

I tried this way:

deq := (2*(y(x)*(diff(y(x), x, x))-1))*(1+(diff(y(x), x))^2)+2*(diff(y(x), x, x))*sqrt(1+(diff(y(x), x))^2)-cos(x)*sqrt(1+(diff(y(x), x))^2)*(1+(diff(y(x), x))^2) = 0; sol := dsolve({deq, y(0) = 0, (D(y))(0) = 0}, y(x), numeric); ynum := proc (x) options operator, arrow; rhs(megold(x)[2]) end proc

so 'ynum(x)' is a function, (I can plot it.) But, then the integral:

int(2*[('ynum(x)'*(diff('ynum(x)', x, x))-1)/sqrt(1+(diff('ynum(x)', x))^2)+(diff('ynum(x)', x, x))/(1+(diff('ynum(x)', x))^2)], x = 0 .. (1/3)*Pi)

but Maple: Error, (in int) wrong number (or type) of arguments: for an operator integrand a range without a variable of integration is expected, got x = 0 .. (1/3)*Pi

I'm a beginner in Maple, so I don't know what's wrong.

Thanks. But I think square brackets are good in my Maple. Anyway I don't even know how to integrate it. The problem is that (I think), that I can't refer to sol as a function.

I tried this way:

deq := (2*(y(x)*(diff(y(x), x, x))-1))*(1+(diff(y(x), x))^2)+2*(diff(y(x), x, x))*sqrt(1+(diff(y(x), x))^2)-cos(x)*sqrt(1+(diff(y(x), x))^2)*(1+(diff(y(x), x))^2) = 0; sol := dsolve({deq, y(0) = 0, (D(y))(0) = 0}, y(x), numeric); ynum := proc (x) options operator, arrow; rhs(megold(x)[2]) end proc

so 'ynum(x)' is a function, (I can plot it.) But, then the integral:

int(2*[('ynum(x)'*(diff('ynum(x)', x, x))-1)/sqrt(1+(diff('ynum(x)', x))^2)+(diff('ynum(x)', x, x))/(1+(diff('ynum(x)', x))^2)], x = 0 .. (1/3)*Pi)

but Maple: Error, (in int) wrong number (or type) of arguments: for an operator integrand a range without a variable of integration is expected, got x = 0 .. (1/3)*Pi

I'm a beginner in Maple, so I don't know what's wrong.