Terminology: General Solutions vs. Particular Solutions

  1. Give the general solution and a particular solution of dy/dt=2y (represent each type of solution with both a formula and a graph). Hint: see the previous note to learn a method for solving this equation.
  2. Provide informal definitions of the terms general solution and particular solution.

  3. Suppose y'=1/(1+t^2).

    1. Determine the general solution y.
    2. Determine the particular solution y(1)=0.

Answer:

  1. The general solution and a particular solution of dy/dt=2y, along with informal definitions of general solution and particular solution, are below.

  2. See image above.
    1. y=arctan(t)+C
    2. y=arctan(t)-pi/4
For a full explanation, have a look at the video below!

Icon for Higher Math Notes: Differential Equations (A Higher Math Help Resource)

Video Explanation

Previous Note

Navigation Tips:

  • To jump to a different lesson, use the navigation at the top of the page.

  • To cycle through the notes in the current lesson, use the Previous Note/Next Note buttons.