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 Math Help > Calculus > Differential Equations

### Contents of this section:

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.