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  3. ZuAI AP College Board Calculus AB/BC
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Finding General Solutions Using Separation of Variables

Benjamin Wright

Benjamin Wright

6 min read

Next Topic - Finding Particular Solutions Using Initial Conditions and Separation of Variables
Study Guide Overview

This study guide covers solving separable differential equations. It explains how to identify these equations (in the form dy/dx = g(x)h(y)), and provides a step-by-step process for solving them using separation of variables and integration. The guide includes practice problems demonstrating the technique and discusses finding general solutions. It also briefly mentions using initial conditions to find particular solutions (covered in a separate guide).

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Previous Topic - Approximating Solutions Using Euler’s MethodNext Topic - Finding Particular Solutions Using Initial Conditions and Separation of Variables

Question 1 of 12

Which of the following differential equations is in a separable form?

dydx=x+y\frac{dy}{dx} = x + ydxdy​=x+y

dydx=xy2\frac{dy}{dx} = xy^2dxdy​=xy2

dydx=x2+y2\frac{dy}{dx} = x^2 + y^2dxdy​=x2+y2

dydx=xy+1\frac{dy}{dx} = \frac{x}{y+1}dxdy​=y+1x​