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.
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.