calculus integration differentiation

[resolved]

there's little help on this subject in the 616 pages User Guide, equally there is little help on this subject in jebem's math tutorials -- that is that I could find. It took me an hour to find that the single quote marks could be used as primes ie y' or y'' other than the templates I have no idea how to enter dx, dy or a dt. How would one enter the following equations in the Prime

dx + x y dy = y^2 dx + y dy

(4x + x y^2 ) dx + (y + x^2 y) dy = 0

or to solve for

y dx - (x + √(y^2 - x^2) dy = 0

(2 x y^4 e^y + 2 x y^3 +y ) dx + (x^2 y^4 e^y - x^2 y^2 - 3x)dy = 0

what solvers would one use????

[parisse]

Divide by dx, you have a differential equation, use desolve. Note that a desolve error can give some interesting information, like for the last one
"Unable to isolate y in exp(y)*x^2*y^3+x^2*y^2+x+y^3*c_1"
which means that the diff eq was solved but the solver was not able to express y in terms of x.