Solving Initial Value Problems with Mathematica's Solver

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Solve each of the following initial value problems using Mathematica.

  1. y″ - 6y′ + 9y = xe3x, y(0) = 1, y′(0) = 0

  2. y″ + 25y = cos(5x), y(0) = 0, y′(0) = 0

  3. y″ + 3y′ + 2y = sin(ex), y(0) = 0, y′(0) = 0

  4. 4y″ - 4y′ + y = ex/2(1 - x2)1/2, y(0) = 0, y′(0) = 0

Mathematica LogoClick on the button provided on the left to switch to a fresh Mathematica document with the form of these problems already entered for you. Come back here to your browser when you are finished.

Mathematica LogoWelcome back! You may be wondering how well you did. Click on the icon on the left to see the answers you should have gotten. (Only the answers are given, so if you don't match our results you need to figure out what you did wrong.)

Hopefully you didn't encounter any insurmountable problems on any of the exercises you just completed. Let's finish up this lab with a few final comments...

 
Compass If you're lost, impatient, want an overview of this laboratory assignment, or maybe even all three, you can click on the compass button on the left to go to the table of contents for this laboratory assignment.