1. Rewrite the given first-order differential equation in normal form. Sketchthe direction field defined by the differential equation either by hands orby using an appropriate software.(a) x' +2x-1=0(b) (t²+1)x' - x = 0KAD

Answered: 1. Rewrite the given first-order…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Related questions

Question

1. Rewrite the given first-order differential equation in normal form. Sketch
the direction field defined by the differential equation either by hands or
by using an appropriate software.
(a) x' +
2x-1=0
(b) (t²+1)x' - x = 0
KAD

Expert Solution

Step 1

What is Differential Equation:

When an equation consists of one or more terms with derivative of a dependent variable with respect to one or more than one independent variable, that very equation is referred to as a differential equation. For a single independent variable, the equation is ordinary whereas for more than one independent variable, the equation is partial. For an ordinary differential equation, the slope field is the graph of its solution curve.

Given:

Given differential equations are:

$\begin{array}{rcl} x' + 2 x - 1 & = & 0 \\ (t^{2} + 1) x' - x & = & 0 \end{array}$