Contents of this section: Differential Equations DE Glossary Homogeneous Linear DE Linear FODE Legendre's Differential Eq CalculusDifferentialChebyshev.aspx Reduction of Order

In this section you will find:

Differential Equation Glossary, defining
    Linear
    Order
    Homogeneous
    Separable
    ...and other terms

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-x²)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 y₁(x) is known to get a linearly independent solution y₂(x).

Internet references

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

Related pages in this website

The webmaster and author of this Math Help site is Graeme McRae.