College · advanced
Differential Equations
First-order methods and the models Diff EQ is built for.
Skills
11 skills in 3 sections — fundamentals first, then more specific topics. Practice each until Mastery Score 100.
A.First-order equations8 skills
- A.1 Slope Fields at a PointPractice →Evaluate y' = f(x, y) at a given point.
- A.2 Solving y' = f(x) with Initial ValuesPractice →Integrate a polynomial slope and use y(0) to find the full solution.
- A.3 Separable ODEs (Setup)Practice →Separate variables for dy/dx = g(x)h(y).
- A.4 y' = ky SolutionsPractice →Write the general solution of exponential growth/decay ODEs.
- A.5 Initial Values & the Constant CPractice →Use y(0) to pin down C in y = Ce^(kt).
- A.6 Equilibrium SolutionsPractice →Find the constant solution of y' = k(y − a).
- A.7 Integrating Factor μPractice →Find μ(x) for y' + P(x)y = Q(x) with constant P.
- A.8 Exact EquationsPractice →Check My or find F for a simple exact ODE.