Ask Me Help Desk - Differential Equation Help needed

#1:

$sec(2x)dy+csc(y)dx=0$

$sec(2x)dy=-csc(y)dx$

Separate variables:

$\frac{dy}{-csc(y)}=\frac{dx}{sec(2x)}$

Now, integrate:

For the other two, I can not read them for certain. Try using ^ (SHIFT 6) if you mean an exponent.

I am going to hazard a guess and presume that #2 is:

$(y^{2}+3xy)dx=(4x^{2}+xy)dy$ ?

#3: $(1-2x^{2}-2y)dy-(4x^{3}+4xy)dx=0$ ?

$M(x,y)=4x^{3}+4xy, \;\ N(x,y)=1-2x^{2}-2y$

Check if $\frac{{\partial}M}{{\partial}y}=\frac{{\partial}N} {{\partial}x}$

If this is true, then it is exact.