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.