Here is one problem filled with multiple little differential equation problems.

1.1 The following differential equation is exact. Find a function(,) whose level curves are solutions to the differential equation =0. F(x,y) =?

1.2 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) =?

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

_____ = constant.

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

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

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

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

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

1.9 Solve the following initial value problem: (dy/dt) + 0.5ty = 2t with(0)=3. y = ?

1.10 Find the general solution of the first-order linear differential equation: y' - (lnx)y = 3x^x .So y(x) = ? Note: UseCfor the arbitrary constant.

1.11 Solve the initial-value problem(/) = ⁶ 5, (0)=2. Therefore y(x) = ?

1.12 Find the general solution to tln(t)(dr/dt) + = 9te^t. Therefor r = ? UseCto denote the arbitrary constant in your answer.

1.13 Find the solution to the initial value problem (1+x¹³)y'+13x¹²y=20x¹⁵. Subject to the conditiony(0)=2.

1.14 Find the function y(t)that satisfies the differential equation (dy/dt) - 2ty = 9t²e^t2

At the end of the equation e is to the power of t^2 so (e^(t^2)). and the condition y(0)=2. So y(t) = ?

1.15 Solve the initial-value problemtlnt(dy/dt)+y = te^t, y(2) = 1. So y(t) = ?