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. Let’s take a look at some examples.

Wolfram|Alpha can show the steps to solve simple differential equations as well as slightly more complicated ones like this one:

Wolfram|Alpha can help out in many different cases when it comes to differential equations. Get step-by-step directions on solving exact equations or get help on solving higher-order equations. Even differential equations that are solved with initial conditions are easy to compute.

What about equations that can be solved by Laplace transforms? Not a problem for Wolfram|Alpha:

This step-by-step program has the ability to solve many types of first-order equations such as separable, linear, Bernoulli, exact, and homogeneous. In addition, it solves higher-order equations with methods like undetermined coefficients, variation of parameters, the method of Laplace transforms, and many more. So the next time you find yourself stuck solving a differential equation or wanting to check your work, consult Wolfram|Alpha!

Hi.

Is this option also available on Mathematica or it’s just for the WolframAlpha?

@ Jose -

This option is available in *Mathematica*. Once you create a Wolfram|Alpha input, put in your query in *Mathematica* the same way you would in Wolfram|Alpha to get the same results.

Follow this link to learn more: http://www.wolfram.com/mathematica/new-in-8/combine-knowledge-and-computation/

Thank you!

Muy util. En aplicaciones como diseño de filtros en electronica y en diseño de sistemas de control. Muchas gracias.

Bearing in mind that the target is to add everything to Wolfram Alpha with a view to getting as near as practicable…I suggest that the emphasis be put on Wolfram Alpha generating the Step by Step information from the actual steps it takes to arricve at its solution. As it is the work involved will prove a significant limiting factor.

I have a problem with the input of the ( ‘ ) to write the Differential equation in the android app. Any solution?

Well, one workaround is to use the generic Android keyboard, which also has the advantage of Swype support. You can change this under Menu -> More -> Preferences.

search the android market for “Hacker’s Keyboard” – it has just about every symbol you can think of.

My teacher was very impressed with this when I showed it to him, little did I know it was such a new feature.

I know that this request is propably way under your league, but what about showing steps when solving two equations with two unknowns, or three EQ with three unknowns etc.. ?

Thanks for a great piece of tech.!

is it possible to make wolfram solve a problem using an specific method like D operator method etc??? if yes plz explain how?!

Neither the app version of wolfram alpha nor pro supports step by step solutions for laplace transformations, inverse laplace, or convolutions as of June 17th 2014 as claimed

Hello, thank you for your comment! Are you trying to solve an ODE? If so, it will show partial steps for Laplace and InverseLaplace.

please solve semi analytically

(y”(x))^3+(1-x)+(y”(x))^2+1=0

For the Differential equation, y”-y+x=0

How is the lagrangian determined?

Thanks for this. How can we interactivity change the boundary conditions ?