How to Multiply Matrices by Each Other
How to Solve Differential Equations Using Op Amps
How to Solve Nonlinear Systems

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.

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