Differential Equations

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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.)


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