Method: Solution to Differential Equations

Step 1: Find the derivative of your given equation.

Step 2: Compare your derivative from Step 1 to the differential equation you were given by the problem.

Your given differential equation may not look like a well solved differential equation. By well solved differential equation I mean the derivative notation is alone on one side of the equals.

• $y^{‘}= \_\_\_\_\_\_\_\_$
• $\frac{\mathit{dy}}{\mathit{dx}}= \_\_\_\_\_\_\_\_$

You may need to substitute both your given equation and the derivative you found in Step 1 into the differential equation you were given in order to “show” or “verify” you have a solution.

If, once you have plugged everything into your differential equation, you find the differential equation is a true statement (i.e., the left side of the equation equals the right side of the equation), then you have “shown” or “verified” that your given equation is a solution to your given differential equation.

If, once you have plugged everything into your differential equation, you find the differential equation is a false statement (i.e., the left side of the equation does not equal the right side of the equation), then you have “shown” or “verified” that your given equation is a not a solution to your given differential equation.