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Math / Differential Equations and Linear Algebra 3 / Chapter 1.1 / Problem 29P

Differential Equations and Linear Algebra | 3rd Edition | ISBN: 9780136054252 | Authors: C. Henry Edwards, David E. Penney

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In , a function y = g(x) is described by some

Chapter 1, Problem 29P

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QUESTION:

Problem 29P

In Problems, a function y = g(x) is described by some geometric property of its graph. Write a differential equation of the form dy/dx = f(x, y) having the function g as its solution (or as one of its solutions).

Every straight line normal to the graph of g passes through the point (0, 1). Can you guess what the graph of such a function g might look like?

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QUESTION:

Problem 29P

In Problems, a function y = g(x) is described by some geometric property of its graph. Write a differential equation of the form dy/dx = f(x, y) having the function g as its solution (or as one of its solutions).

Every straight line normal to the graph of g passes through the point (0, 1). Can you guess what the graph of such a function g might look like?

ANSWER:

Solution

Step 1 of 4

In this problem, we have to write the differential equation of the form $\frac{dy}{dx}=f(x,\ y)$ having the function $g$ as its solution.

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