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Chapter 6: Q10E (page 252)

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

Short Answer

Expert verified

Answer:

Therefore, the two solutions of the given differential equation are:

Step by step solution

01

Given information

The given equation is:

02

Find differential equation solution form


03

Find the first and second derivative

Summation indexforandfor.

04

Substituting equations (1), (2), and (3)


05

Find coefficients of the series

06

Conclusion

Therefore, the two solutions of the given differential equation are;

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Most popular questions from this chapter

In Problems 1 and 2 without actually solving the given differential

equation, find the minimum radius of convergence of power series solutions about the ordinary point. About the ordinary point

In Problems, 31-34 verify by direct substitution that the given power series is a solution of the indicated differential equation. [Hint: For a power

Bessel’s Equation

In Problems 1-6 use (1) to find the general solution of the given differential equation on (0,∞).

6. ddx[xy']+(x-4xy)=0

In Problems, 3–6 find two power series solutions of the given differential equation about the ordinary point x 5 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.

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

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