# What does differential equations with constant coefficient mean?

I read the definition of differential equations with constant coefficient.

I am very confuse.

What does it mean? What are some example?

• Can you tell us what definition you read? Where did you read it? Was there really no example after the definition? Nov 17 '16 at 8:30
• A differential equations with constant coefficients means a differential equation in which the coefficients are constants. Which part of this do you need help with, Bob? By the way, congratulations on that Nobel Prize. Nov 17 '16 at 9:00
• ax'' + bx'+cx = 0 Nov 17 '16 at 9:02
• so a, b, c are constant? Nov 17 '16 at 9:03
• Yes, I am a genious. Thanks. Nov 17 '16 at 9:03

A linear second-order ODE is an equation of the form $$a(x)u''(x)+b(x)u'(x)+c(x)u = f(x),$$ where $u \colon I \to \mathbb{R}$ is the unknown defined on some interval $I \subset \mathbb{R}$, and $a$, $b$, $c$, and $f$ are given functions defined on $I$.
The equation has constant coefficients if $a$, $b$ and $c$ are constant functions throughout $I$ (but not $f$).