**
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.

- ${\textcolor[rgb]{}{y}}^{\textcolor[rgb]{}{\u2018}}\textcolor[rgb]{}{=}\textcolor[rgb]{}{}\textcolor[rgb]{}{\_}\textcolor[rgb]{}{\_}\textcolor[rgb]{}{\_}\textcolor[rgb]{}{\_}\textcolor[rgb]{}{\_}\textcolor[rgb]{}{\_}\textcolor[rgb]{}{\_}\textcolor[rgb]{}{\_}$
- $\frac{\textcolor[rgb]{}{\mathit{dy}}}{\textcolor[rgb]{}{\mathit{dx}}}\textcolor[rgb]{}{=}\textcolor[rgb]{}{}\textcolor[rgb]{}{\_}\textcolor[rgb]{}{\_}\textcolor[rgb]{}{\_}\textcolor[rgb]{}{\_}\textcolor[rgb]{}{\_}\textcolor[rgb]{}{\_}\textcolor[rgb]{}{\_}\textcolor[rgb]{}{\_}$

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.

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