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(a) Use a computer algebra system to draw a direction field for the differential equation. Get a printout and use it to sketch some solution curves without solving the differential equation.(b) Solve the differential equation.(c) Use the CAS to draw several members of the family of solutions obtained in part (b). Compare with the curves from part (a).$ y' = y^2 $

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a)See Graph b)See Graphc) where $K=-C . y=0$ is also a solution.

Calculus 2 / BC

Chapter 9

Differential Equations

Section 3

Separable Equations

Campbell University

Oregon State University

Baylor University

University of Nottingham

Lectures

13:37

A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. An ordinary differential equation (ODE) is a differential equation containing one or more derivatives of a function and their rates of change with respect to the function itself; it can be used to model a wide variety of phenomena. Differential equations can be used to describe many phenomena in physics, including sound, heat, electrostatics, electrodynamics, fluid dynamics, elasticity, quantum mechanics, and general relativity.

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$$\begin{array}{l}{\text {…

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(a) Use a computer algebra…

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for this problem, we were asked to impart a, use a computer algebra system to draw the direction field for the differential equation why prime of X equals Y squared. So this is the direction field shown here, or actually we can change this. So the it's more explicitly a direction field, not just a slope field. So this gives a bit a little bit of an idea of what the direction field looks like. Then for part B were asked to use um or were as to solve the differential equation. It's rather simple differential equation to solve directly. It's completely it's completely separable. So this is the solution, we get Y of X equals one over C, one minus X. And then lastly, we were asked to use the CIA's to draw several members of the family of the curves. And we have exactly that shone down here, we have a sample solution family.

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