AP Calculus AB · Unit 7: Differential Equations
7.6 Finding General Solutions Using Separation of Variables
In short
You are expected to find general solutions to differential equations by using the method of separation of variables. This involves algebraically separating the variables so that all terms involving the dependent variable are on one side with its differential, and all terms involving the independent variable are on the other side with its differential.
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What else do you need to know about Finding General Solutions Using Separation of Variables?
You then apply antidifferentiation to both sides. The focus in this topic is strictly on finding the general solution, which must include a constant of integration, rather than finding particular solutions using initial conditions (which is covered in a subsequent topic).
Can you do these?
- I can use antidifferentiation to find the general solution to a differential equation.
How is Finding General Solutions Using Separation of Variables tested on the exam?
On the AP Exam, you must explicitly show the separation of variables. Failure to separate variables or omitting the constant of integration severely limits the number of points you can earn on free-response questions. A common error examiners note is students assuming that all differential equations involving fractions will result in logarithmic solutions, which is not always the case. You must carefully apply the correct antidifferentiation rules based on the separated integrand.
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Finding General Solutions Using Separation of Variables: common questions
What do you need to know about Finding General Solutions Using Separation of Variables for AP Calculus AB?
You are expected to find general solutions to differential equations by using the method of separation of variables. This involves algebraically separating the variables so that all terms involving the dependent variable are on one side with its differential, and all terms involving the independent variable are on the other side with its differential.
How is Finding General Solutions Using Separation of Variables tested on the AP Calculus AB exam?
On the AP Exam, you must explicitly show the separation of variables. Failure to separate variables or omitting the constant of integration severely limits the number of points you can earn on free-response questions.
How do I know I have mastered Finding General Solutions Using Separation of Variables?
Check you can do each of these: use antidifferentiation to find the general solution to a differential equation.
Where does Finding General Solutions Using Separation of Variables fit in AP Calculus AB?
Finding General Solutions Using Separation of Variables is topic 7.6 in Unit 7: Differential Equations of AP Calculus AB.
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