Differential Equations — Formula Sheet

dy/dx = g(x), where y = f(x)

Order = highest order derivative present

Degree = highest power of the highest order derivative, only if the equation is polynomial in derivatives

y = a sin(x + b)

y = 2 sin(x + π/4)

dy/dx = h(y)·g(x)

(1/h(y)) dy = g(x) dx

∫(1/h(y)) dy = ∫g(x) dx

H(y) = G(x) + C

F(λx, λy) = λ^n F(x, y)

dy/dx = F(x,y), where F is homogeneous of degree zero

y = v·x

dy/dx = v + x(dv/dx)

x(dv/dx) = g(v) - v

The variable separable form is dy/dx = h(y)·g(x).

F1(x,y)=y^2+2xy is homogeneous of degree 2.

F2(x,y)=2x-3y is homogeneous of degree 1.