**
Step 1:
** Identify your two variables.

**
Step 2:
** Separate your equation by variables on to either side of the equals.

This will mean treating your differential *
notation
*, $\frac{\textcolor[rgb]{}{\mathit{dy}}}{\textcolor[rgb]{}{\mathit{dx}}}$, like two variables being divided. You will would want the $\textcolor[rgb]{}{\mathit{dx}}$ piece to be on the side with the *
x’s
*, or the $\textcolor[rgb]{}{\mathit{dy}}$ piece to be on the side with the *
y’s
*, or the $\textcolor[rgb]{}{\mathit{dt}}$ to be on the side with the*
t’s
*. Make sure that you are always multiplying or dividing variables by the $\mathit{dx},\mathit{dy},\mathit{dt}$ piece. You are about to take an antiderivative, and an antiderivative is normally of the form $\int \mathit{equation\; dx}$. You are never adding or subtracting your $\mathit{dx},\mathit{dy},\mathit{dt}$ piece.

**
Step 3:
** Take the antiderivative of both sides of the equation.

This antiderivative process will be the same as a standard indefinite integral process. You will only need a single *
+C
* value that will work for both antiderivatives. It is best to put this *
+C
* on the independent variable side (*
x
*-variable) of the equation. Although it does not matter at this step of the process which side you choose.

**
Step 4:
** Solve the equation you found in *
Step 3
* to get the dependent variable (*
y
*-variable) alone on one side of the equals.

**
Step 5 (If asked to find a particular solution):
** Sometimes you will be given an actual value or point that the solution needs to go through (i.e., an $(\textcolor[rgb]{}{x},\textcolor[rgb]{}{y})$). You will use that value to find the *
+C
* value for your specific situation. This is just like the method you would apply in an initial value problem you learned earlier.

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