Differential Equations

Given the differential equation $$\frac{\text{d}P}{\text{d}t}=5P$$  
A) Find the general solution for P to the differential equation
B)Find the particular solution for P to the differential equation given P(0)= 418

Solve the differential equation  $$\frac{\text{d}y}{\text{d}t}=\frac{3t^2}{y}$$  with initial condition  𝑦(2) = 0.

What would the sign of the square root solution to a differential equation be given the initial condition g(1)= -5?

$$\frac{\text{d}y}{\text{d}x}=\tan x+15x^2+e^x+\frac{1}{x}$$

$$\frac{\text{d}y}{\text{d}x}=\frac{4x}{y}$$ Suppose y(0)=1.
The particular solution is

In drawing the slope field for the differential equation , I would place short slope lines of _________ at the points (0,1), (1,-1), and (2,-2)
  $$\frac{dy}{dx}=2x-3y$$  

Select all that apply

Which slope field is represented by  $$\frac{\text{d}y}{\text{d}x}=x^2$$ ?

Which of the following is the solution to the differential equation $$\frac{dy}{dx}=\frac{x^2}{y}$$  with the initial condition y(3) = -2?

Which of the following differential equations corresponds to the slope field shown?

The learning rate for new skills is proportional to the difference between the maximum potential for learning that skill, M, and the amount of the skill already learned, L. Which equation describes the relationship?