Wolfram Alpha now solves differential equations with step-by-step solutions! They describe the new feature accordingly:
Wolfram|Alpha has become well-known for its ability to perform step-by-step math in a variety of areas. Today we’re pleased to introduce a new member to this family: step-by-step differential equations. Differential equations are fundamental to many fields, with applications such as describing spring-mass systems and circuits and modeling control systems.
From basic separable equations to solving with Laplace transforms, Wolfram|Alpha is a great way to guide yourself through a tough differential equation problem.
See examples and more on the Wolfram Alpha Blog.
Traffic statistics is yet another topic that Wolfram|Alpha can analyze. The Wolfram|Alpha blog gives some examples for the usage.
New York City. Los Angeles. Chicago. Each of these cities is renowned for a diverse array of cultural, entertainment, culinary, and other experiences—as well as for legendary traffic delays. But just how bad do native commuters have it? And if you drive to work in a different city, how does your commute stack up? Wolfram|Alpha can’t yet guide you through the traffic, but it can visualize and compare statistics about traffic and urban transportation in more than 100 US urban areas, with data from the Texas Transportation Institute’s Urban Mobility Report.
Wolfram|Alpha is becoming a more valuable tool for engineers practically every day. If you haven’t used it before, you should definitely check it out. Their goals are summarized on their info page:
Wolfram|Alpha’s long-term goal is to make all systematic knowledge immediately computable and accessible to everyone.
We aim to collect and curate all objective data; implement every known model, method, and algorithm; and make it possible to compute whatever can be computed about anything. Our goal is to build on the achievements of science and other systematizations of knowledge to provide a single source that can be relied on by everyone for definitive answers to factual queries.
Wolfram|Alpha aims to bring expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels.
Our goal is to accept completely free-form input, and to serve as a knowledge engine that generates powerful results and presents them with maximum clarity.
Wolfram|Alpha is an ambitious, long-term intellectual endeavor that we intend will deliver increasing capabilities over the years and decades to come.
With a world-class team and participation from top outside experts in countless fields, our goal is to create something that will stand as a major milestone of 21st century intellectual achievement.
You can do a lot with it. It can definitely serve as a quick replacement when you need to consult an infrequently-used table for some data. What is the bulk density of sand? Need to know the coefficient of thermal expansion for Copper? What about the general properties of elemental Silicon? Need to solve some engineering problems? These examples only scratch the surface of the large number of topics that Wolfram|Alpha covers.