Measuring Volume Under a Surface Using a Double Integral
How to Use a Partial Derivative to Measure a Slope in Three Dimensions
Solving Differential Equations Using an Integrating Factor

Checking Differential Equation Solutions

Even if you don’t know how to find a solution to a differential equation, you can always check whether a proposed solution works. This is simply a matter of plugging the proposed value of the dependent variable into both sides of the equation to see whether equality is maintained.

For example, here’s a differential equation with a dependent variable y:

image0.png

You may not have a clue how to begin solving this differential equation, but imagine that an angel lands on your pen and offers you this solution:

y = 4e3x sin x

You can check to see whether this angel really knows math by plugging in this value of y as follows:

image1.png

Because the left and right sides of the equation are equal, the angel’s solution checks out.

  • Add a Comment
  • Print
  • Share
blog comments powered by Disqus
How to Multiply Matrices by Each Other
How to Solve Linear Systems Using Substitution or Elimination
Evaluating Double Integrals
Describe Second-Order Circuits with Second-Order Differential Equations
How to Solve a System of Equations Using the Inverse of a Matrix
Advertisement

Inside Dummies.com