put function arguments in parentheses: sin(x) -- correct, sin x -- incorrect; do not omit multiplication: x*sin(x) -- correct, x sin(x) -- incorrect.
Usual keywords are lowercase, which are different from uppercase, e.g. sin is different from Sin. Its default variable is small letter x, but its default index variable in discrete math is k.
By default, the unknown function is y(x) and its initial value is y(0)=0. An independent variable is x for ordinary differential equation.
For a partial differential equation, the unknown function is y(1,x) and y(1,t) with its two independent variables x and t.
For a system of equations, two unknown functions are x(t) and y(t) with an independent variable t.
There are 6 way to input derivative of y: y(1,x), ds(y,x), d(y(x),x), ds(y), d(y(x)), y'
There are 3 way to input second order derivative of y: y(2,x), ds(y,x,2), d(y(x),x,2)
There are 3 way to input the 0.5 order derivativeof y: y(0.5,x), ds(y,x,0.5), d(y(x),x,0.5)
There are 4 way to input the 0.5 order integral of y: y(-0.5,x), ds(y,x,-0.5), d(y(x),x,-0.5), ints(y,x,0.5)