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Differential Equations

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Contents:
Title and Synopsis
Basics
Try It!
Elementary School
Middle and High School
Calculus
Combinatorics
Linear Algebra
Differential Equations
Other Advanced Topics
It's Not (Only) About Math!
More Examples (and Data!)
Less Is More
So Is It Perfect Yet?
What About Google?
Possible Implications
A Threat?
Resources

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Consider the query "d^2 y/dx^2 + 4dy/dx + 5y = 0." Wolfram|Alpha interprets this as a second-order linear differential equation and provides the general solution and plots of individual solutions. If you prefer an initial value problem, try "y''+y=0, y(0)=2, y'(0)=1."

If you want a nonhomogeneous example, try "y''(t) + y(t) = sin t." Here's a nonlinear example: "f'(t) = f(t)^2 + 1." And here's an example involving a parameter: "y'(t)=a t y(t)." Wolfram|Alpha knows the Bessel functions--try "(-4+x^2) w(x)+x w'(x)+x^2 w''(x) = 0." (But following the links for further information about Bessel's equation or either of the two types of Bessel functions involved will take you out of this article.)

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[Note: Contents of frame come from wolframalpha.com and are not maintained by Loci]