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A First Course In Differential Equations With Modelling Applications

Dennis G. Zill

$Math Studyset Vaia Explanations$ Math

11th Edition · 400 pages

ISBN: 9781305965720

Chapter 6: Q8E (page 252)

Find two power series solutions of the given differential equation about the ordinary point

Short Answer

Expert verified

Answer:

The solution is;

Step by step solution

given information

The given equation is:

Step 2: should be distributed into a summation

substitute is raised to

Summation starts at

Summation originally starts atand takes out values forand Summation originally starts at

Combine summations and find coefficients

Determine coefficients for case 1 and case 2

Case 1: Letand

Case 2:Letand

Find two solutions

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Most popular questions from this chapter

In Problems 13 and 14, x= 0 is a regular singular point of the given differential equation. Use the general form of the indicial equation in (14) to nd the indicial roots of the singularity. Without solving, discuss the number of series solutions you would expect to nd using the method of Frobenius.

$x^{2} y'' + (\frac{5}{3} x + x^{2}) y' - \frac{1}{3} y = 0$

In Problems 21 and 22 the given function is analytic at $a = 0$ . Use appropriate series in (2) and long division to find the first four nonzero terms of the Maclaurin series of the given function.

$t a n x$

In Problems 3–6 find two power series solutions of the given differential equation about the ordinary point $x = 0$ .Compare the series solutions with the solutions of the differential equations obtained using the method of Section 4.3. Try to explain any differences between the two forms of the solutions.

$y^{''} - y = 0$

In Problems 11-16 use an appropriate series in (2) to find the Maclaurin series of the given function. Write your answer in summation notation.

$\frac{1}{2 + x}$

In Problems, 35-38 proceed as in Example 4 and find the $ power series solutionof the given linear first order differential equation.

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Find two power series solutions of the given differential equation about the ordinary point

Short Answer

Step by step solution

given information

Step 2: should be distributed into a summation

substitute is raised to

Combine summations and find coefficients

Determine coefficients for case 1 and case 2

Find two solutions

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Most popular questions from this chapter

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