1. (a) Use the "mixed partials" check to see if the following differential equation is exact. If it is exact find a function(,) whose level curves are solutions to the differential equation (4^x sin()+4)+(62cos()) = 0. Is it exact or not exact and F(x,y) =?

(b) Solve the following differential equation: 2(/)=22+6²

_____ = constant.

(c) Solve the following initial value problem: ((3y²-t²)/y⁵)(dy/dt) + (t/2y⁴) = 0; y(1) = 3 So ______ = 0.

(d) Solve the following differential equation: (⁵)+(+⁵)=0. ______ = constant.

(e) Solve the following differential equation: ((ydx+xdy)/(1x²y²)) + xdx = 0. ______ = constant.

(f) Solve the following initial value problem: 8(dy/dt) + y = 8t with(0)=6. (Find yas a function oft.) y = ?

(g) Find the function satisfying the differential equation: 4=3⁵ and y(0) = -5. So y = ?