Answer theas question

(1) Both equations in (a) and (b) are separable.

(a)

Expand both sides into partial fractions.

Integrate both sides:

(You could solve for y explicitly, but that's just more work.)

(b)

Integrate both sides:

(2)

(a)

Multiply both sides by an integrating factor, sec(x) + tan(x) :

Integrate both sides and solve for y :

(b)

(Note that the right side is also written as sinh(x).)

Multiply both sides by e ˣ :

Integrate both sides and solve for y :

(c) I've covered this in an earlier question of yours.

(d)

Multiply through the right side by x/x :

Substitute y(x) = x v(x), so that y' = xv' + v, and the DE becomes separable: