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Appendix F Selected Hints
1 What is a Differential Equation?
1.5 Exercises
🏋️♂️ Practice Drills
Exercises
1. Identify the Differential Equations.
1.a
Hint.
There are only 5 Differential Equations in this set.
3. Identify the Coefficients.
3.b
Hint.
Look for the dependent variable in each term. The coefficient is the constant or function that multiplies the dependent variable.
2 Classification
2.4 Exercises
🏋️♂️ Practice Drills
Exercises
1. Identify the Linear & Nonlinear Terms.
1.e
2. Identify the Linear & Nonlinear Differential Equations.
2.f
Hint.
Remember that a linear differential equation contains only linear terms. Four of these equations are linear.
2.g
Hint.
First identify the dependent variable, then carefully look at each term to determine if it is nonlinear.
5 Separation of Variables
5.5 Exercises
💡 Conceptual Quiz
Exercises
1. True or False.
1.i 👍👎.
Hint.
Check to see that the differential equation is first order and separable.
1.j 👍👎.
Hint.
Check to see that the differential equation is first order and separable.
6 Integrating Factor
6.1 Exercises
💡 Conceptual Quiz
6.1.1.
6.1.1.a 👍👎.
Hint.
Check to see that the differential equation is in the form
\(y'+P(x)y=Q(x)\text{.}\)
🏋️♂️ Practice Drills
6.1.1. Identifying Equations for the IF Method.
Hint.
A first-order linear equation has
\(y\) and
\(y'\) only to the first power and not inside nonlinear functions.
9 Homogeneous Equations (LHCC)
9.6 Exercises
🏋️♂️ Practice Drills
9.6.1. Identifying LHCC Equations.
9.6.1.f Select the LHCC Equations.
Hint.
There are only 4 LHCC equations in this set.
