Many students have a lot of trouble solving differential equations because they get hung with some of the algebra steps they need to follow.
Cut apart the problems from their seven or eight steps and their seven or eight reasons. Place the pieces in a small envelope. You will have ten envelopes of differential equations and their solutions. When students receive an envelop they will open the envelop and try to solve the differential equation for a particular solution in the form y = f(x) so that it passes through a given point.
Distribute an envelope to a student or a pair of students. They should open the envelope and remove the pieces from the envelope. After they spread out the reasons and steps, they should try to reorganize the steps and reason to show how the particular solution can be found.
After they have solved the differential equation, they can record their solution on a sheet of paper and then return the puzzle pieces to the envelope. Students can then switch problems with another student or pair or students.
This type of activity can help students who are struggling with the algebraic steps in solving a differential equation.
The last page of the file is a blank chart that can be used to make other sorting exercises.
The exercises have been numbered and an answer key has been included.
You can differentiate this lesson by
• Removing all the reasons and have the students fill those in
• Removing all the algebraic steps and have the students fill those in;
• Removing some of the reasons and have the students fill them in;
• Removing some of the algebraic steps and have the students fill them in.
• Remove the final algebraic step and give the students three possible answers to see if they can reason which equation is the correct solution.
After students have solved all these differential equations you can make up additional problem and place them on the blank form and students can use the blank form as an organizer for their solution. Students should be able to remember the reasons from their experiences with this activity.