I read the definition of differential equations with constant coefficient.
I am very confuse.
What does it mean? What are some example?
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$\begingroup$ Can you tell us what definition you read? Where did you read it? Was there really no example after the definition? $\endgroup$– Mariano Suárez-ÁlvarezNov 17, 2016 at 8:30
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1$\begingroup$ 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. $\endgroup$– Gerry MyersonNov 17, 2016 at 9:00
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$\begingroup$ ax'' + bx'+cx = 0 $\endgroup$– Bob DylanNov 17, 2016 at 9:02
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$\begingroup$ so a, b, c are constant? $\endgroup$– Bob DylanNov 17, 2016 at 9:03
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$\begingroup$ Yes, I am a genious. Thanks. $\endgroup$– Bob DylanNov 17, 2016 at 9:03
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1 Answer
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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 $f$).
