Modeling with differential equations

  • #1

Homework Statement


a) What can you say about a solution of the equation y' = -y^2 just by looking at the differential equation?
b) Verify that all members of the family y = 1/(x + C) are solutions of the equation in part (a)
c) Can you think of a solution of the differential equation y' = -y^2 that is not a member of the family in part (b)?
d) Find a solution of the initial-value problem:
y' = -y^2 y(0) = 0.5


Homework Equations


Well for part b do I take the derivative of y? Other than that I don't believe there are specific equations.


The Attempt at a Solution


For part (a) I set -y^2 = 0 and got that a solution is y = 0. Not positive if that's what it's asking, however.
I'm not positive if I have to take the derivative in part (b), and I don't really know where to start for the rest.
 

Answers and Replies

  • #2
Stephen Tashi
Science Advisor
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The Attempt at a Solution


For part (a) I set -y^2 = 0 and got that a solution is y = 0. Not positive if that's what it's asking, however.
What is not positive, you or y' ?
I'd say y' can't be posiitive so the solution are curves that are flat or slope downwards.
I'm not positive if I have to take the derivative in part (b)
The usual way to test if a specific function is a solution is to substitute it into the equation. That would involve taking the derivative when you substittue for y'
and I don't really know where to start for the rest.
c) You already thought of one solution Y = 0, although I don't think the way you derived it
made sense.

d) Use the form of the solution that they gave you, y(x) = 1/(x + C). Set x = 0 and solve for the value of C that makes y(0) = 0.5.
 

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