Homogeneous Linear DE — e.g.
ay'' + by' +
cy = 0, where a,b,c are constants
Linear FODE -- e.g. a(x) y' + b(x) y = c(x), and y' + p(x) y =
q(x); Specific examples include
y' = ax + by + c
ay' - y'x + y + b = 0
cot(x) y' + y = csc(x)
Second order ordinary differential equations
Legendre's Differential Equation: (1-x^{2})y''−2xy'+n(n+1)y=0
Chebyshev's equations
(1-x²)y" - xy' + n²y = 0 and
(1-x²)y" - 3xy' + n(n+2)y = 0, where n is a real
constant.
Reduction of order,
when one solution y_{1}(x) is known to get a linearly independent
solution y_{2}(x).
SOS Math: Differential
Equations, which has a large number of links to other pages in that website,
including
SOS Math: First
Order Linear Equations of the form y' + p(x) y = q(x)
SOS Math: Separable
Equations of the form y' = f(x,y) where f(x,y) can be written h(x) g(y), so
that dy/g(y) = h(x) dx
SOS Math: Homogeneous
Linear Equations of the form ay'' + by' + cy = 0, where a,b,c can be
functions of x