Solving Differential Equations (Leaving Cert Applied Maths): Flashcards

Equations containing derivatives like $\frac{dy}{dx}$

Has $\frac{dy}{dx}$ as highest derivative

Has $\frac{d^2y}{dx^2}$ as highest derivative

Type 1: general, Type 2: initial cond., Type 3: 2nd order

Solution with arbitrary constant of integration

Uses initial conditions to find specific value of c

Separate variables, integrate both sides, rearrange for y

Use initial condition to find c, then substitute back

Let $v = \frac{dy}{dx}$, then $\frac{dv}{dx} = \frac{d^2y}{dx^2}$

Get all y terms one side, all x terms other side

$\ln x + c$

$e^x + c$