3 ✅EASY✅ steps for solving 👈SEPARABLE👉 differential equations #apcalculus #apcalc #unit7 #shorts

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In Topic 7.6 of AP Calculus, we dive into the procedure for solving separable differential equations, which are differential equations in which the variables can be fully separated onto different sides of the equation (all the x variables on one side, and all the y variables on the other side).

The first step is to rearrange the differential equation so that all terms containing one variable are on one side of the equation, and all terms containing the other variable are on the opposite side. Once the variables are separated, the next step is to integrate both sides of the equation. This integration should be done with respect to the variable present on each side of the equation.

The final step is to solve the integrated equation for the dependent variable, which is usually y. This might involve algebraic manipulation to isolate y and express it in terms of x. By following these steps consistently, we can find the general solution to any separable differential equation.

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Unit 7 of AP Calculus is all about Differential Equations:
7.1 Modeling Situations with Differential Equations
7.2 Verifying Solutions for Differential Equations
7.3 Sketching Slope Fields
7.4 Reasoning Using Slope Fields
7.5 Approximating Solutions Using Euler's Method (BC only)
7.6 Finding General Solutions Using Separation of Variables
7.7 Finding Particular Solutions Using Initial Conditions and Separation of Variables
7.8 Exponential Models with Differential Equations
7.9 Logistic Models with Differential Equations (BC only)

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