Each card is a single, complete idea: what it is, the formulas you need, and one worked example. Built to be re-read.
Move all y terms to one side and all x terms to the other, then integrate both sides.
A differential equation relates a function to one or more of its derivatives. To verify that a proposed function is a solution, differentiate it and plug both the function and its derivative(s) back into the equation. If both sides simplify to the same expression, the function satisfies the equation.
A slope field draws short line segments at grid points to show the slope prescribed by a differential equation. Use the field to sketch solution curves that follow the flow, and match equations to fields by looking for global sign patterns (for example, dxdy=x2+y2 never produces negative slopes).
When a differential equation can be written with all y terms on one side and all x (or t) terms on the other, integrate both sides. Add the constant of integration on the independent-variable side, then use an initial condition to solve for the particular solution.
The rate-of-change model dtdy=ky describes quantities that grow or decay in proportion to their current size. Its solution is y=Cekt, where C is the initial value and k is determined by additional data points.