Solving & Interpreting Differential Equations (Edexcel A-Level Mathematics): Flashcards

An equation involving the first derivative of an unknown function.

Separate variables, integrate both sides, solve for $y$.

$\frac{dy}{dx} + P(x)y = Q(x)$.

It simplifies a linear differential equation for integration.

They involve the second derivative of the unknown function.

Substitute $y = e^{mx}$ into the differential equation.

The nature of the roots of the characteristic equation.

Relate it back to the physical context of the problem.

They help find specific values for constants in the solution.

It provides insight into the system's long-term behavior.