Purchase Solution

Differential Equations Problem Set

Not what you're looking for?

Ask Custom Question

Consider the differential equation

dy/dx = -x/y.

a) Sketch a direction field for this differential equation.
b) Sketch solution curves of the equation passing through the points (0, 1), (1, 1) and (0, -2).
c) State the regions of the xy-plane in which the conditions of the existence and uniqueness theorem are satisfied. Quote the theorem which you are using.
d) Consider the autonomous equation

dx/dt = -3/2 * third root of x.

Show that the trajectory passing through a point x_0 > 0 reaches a fixed point in finite time. Explain why it is possible in this case to have more than one trajectory passing through a point of the phase space.

Please refer to the attached document for the complete problem set.

Attachments
Purchase this Solution

Solution Summary

This solution shows step-by-step calculations to solve various problems involving ordinary differential equations. Explanations are also included for understanding.

Solution Preview

(a) We wish to sketch a direction field for this differential equation.

We do so by drawing the vector (y, -x) at each point (x, y). The result is shown ...

Purchase this Solution


Free BrainMass Quizzes
Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.