solve the differential equation duu? +4dt12+4°6.

Consider the given differential equation, dudt=u2+4t2+4 Write the given differential equation in…

Answered: dt 1²+4 6.

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dt 1²+4 6.

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.1: Lines

Problem 2ECP

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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

solve the differential equation

With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.

Expert Solution

Step 1

Consider the given differential equation,

$\frac{d u}{d t} = \frac{u^{2} + 4}{t^{2} + 4}$

Write the given differential equation in variable separable form.

$\Rightarrow d u = \frac{u^{2} + 4}{t^{2} + 4} d t \Rightarrow \frac{d u}{u^{2} + 4} = \frac{d t}{t^{2} + 4} . . . . . . . . . . . . . . . . . . . . . (1)$

The differential equation is in variable separable form.

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