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Placement Test Practice — Differential Equations
Placement Test Practice — Differential Equations
Practice Test — 16 Questions
1. What is the order of $y'''+y=0$?
2. What does $y(0)=3$ mean?
3. Solve $y'=2x$.
4. Solve $y'=4y$.
5. Solve $y'=ky$ in words.
6. What is a slope field?
7. What is the integrating factor for $y'+y=1$?
8. Write the standard form of a first-order linear equation.
9. What does separable mean?
10. What kind of behavior does $y''+\omega^2 y=0$ model?
11. In motion, what is $y'$?
12. In motion, what is $y''$?
13. Solve $y'=3y$ with $y(0)=2$.
14. Why are initial conditions used?
15. What happens when the integrating-factor method works?
16. Give one application of differential equations.
Show Answer Key
1. Third order
2. The solution passes through $(0,3)$
3. $y=x^2+C$
4. $y=Ce^{4x}$
5. Exponential growth or decay depending on the sign of $k$
6. A picture of slopes for possible solution curves
7. $e^x$
8. $y'+P(x)y=Q(x)$
9. Variables can be split and integrated on opposite sides
10. Oscillation
11. Velocity or first rate of change
12. Acceleration or second rate of change
13. $y=2e^{3x}$
14. To choose one specific solution from a family
15. The left side becomes the derivative of a product
16. Population growth, cooling, springs, circuits, and many others