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Calculus / Fundamentals of Differential Equations 8 / Chapter 1.2 / Problem 19E

Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider

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Show that the equation (dy/dx)2 +y2 +4 = 0 has no

Chapter 1, Problem 19E

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QUESTION:

Problem 19E

Problem

Show that the equation (dy/dx)2 +y2 +4 = 0 has no (real-valued) solution.

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QUESTION:

Problem 19E

Problem

Show that the equation (dy/dx)2 +y2 +4 = 0 has no (real-valued) solution.

ANSWER:

Solution:

Step 1:

In this problem we need to show that the equation $(\frac{dy}{dx}{)}^{2}\ +{y}^{2}+4=0$ has no (real valued) solution.

Given equation is $(\frac{dy}{dx}{)}^{2}\ +{y}^{2}+4=0$

$\Rightarrow{}(\frac{dy}{dx}{)}^{2}=\ -({y}^{2}+4)$

$\Rightarrow{}\frac{dy}{dx}\ =\sqrt{(-1)({y}^{2}+4)}$

$\Rightarrow{}\frac{dy}{dx}=i\sqrt{{y}^{2}+4}$ , since $(-1)=(i{)}^{2}\Rightarrow{}\sqrt{(-1)}=i$

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