Differential Equations

Topics in this chapter

• Differential Equation Basics
• Formation by Eliminating Constants
• Variable-Separable Equations
• Homogeneous First-Order Equations
• Linear Equations and Integrating Factors
• Bernoulli Differential Equations
• General Solutions and Verification
• Initial-Value Problems

Cheat sheet

Practice questions

1. Question 1Q-14B8D2

   For the differential equation ((d²y/dx²)^3) + ((dy/dx)^5) + y = 0, what are its order and degree?

   1. A.Order 1, degree 3
   2. B.Order 2, degree 3
   3. C.Order 2, degree 5
   4. D.Order 3, degree 2
   See the answer and solution
2. Question 2Q-45BA89

   Find the solution of dy/dx = (1 + y²)/(1 + x²), given that y = 0 when x = 0.

   1. A.y = x
   2. B.y = tan x
   3. C.y = x²
   4. D.y = arctan x
   See the answer and solution
3. Question 3Q-4A5852

   The general solution of dy/dx + y tan x = sin x, on an interval where cos x is non-zero, is:

   1. A.y = C sec x + cos x
   2. B.y = cos x(C − ln|cos x|)
   3. C.y = sin x(C + ln|sin x|)
   4. D.y = C cos x + sin x
   See the answer and solution
4. Question 4Q-146095

   Form a differential equation by eliminating the arbitrary constants from y = C₁eˣ + C₂e⁻ˣ.

   See the answer and solution
5. Question 5Q-DBE80D

   The solution of the differential equation dy/dx = 2xy satisfying y(0) = 3 is:

   1. A.y = 3e^(x²)
   2. B.y = 3e^(2x)
   3. C.y = 3x²
   4. D.y = e^(3x²)
   See the answer and solution