# What is Series solution: Definition and 110 Discussions

In mathematics, the power series method is used to seek a power series solution to certain differential equations. In general, such a solution assumes a power series with unknown coefficients, then substitutes that solution into the differential equation to find a recurrence relation for the coefficients.

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46. ### MHB Series Solution for DE: A Guide to Solving with Zill's Book

Hey! I'm having problems with finding the general solution of this DE, using series. I have readed the Zill book, but I don't know how to start solving. Any help is appreciated! y'' - 4xy' -4y = e^x
47. ### Series solution about a regular singular point (x=0) of xy''-xy'-y=0

Homework Statement Find the indicial equation and find 2 independent series solutions for the DE: xy''-xy'-y=0 about the regular singular point x=0 Homework Equations y=Ʃ(0→∞) Cnxn+r y'=Ʃ(0→∞) Cn(n+r)xn+r-1 y''=Ʃ(0→∞) Cn(n+r)(n+r-1)xn+r-2 The Attempt at a Solution Finding the...
48. ### Theoretical/non-tedious question about power series solution of y'' + y = 0

1. "Homework Statement Find a recurrence formula for the power series solution around x = 0 for the differential equation given in the previous problem." The previous problem says: "Determine whether x = 0 is an ordinary point of the differential equation y'' + y = 0." Homework...
49. ### Series Solution Near an Ordinary Point

Homework Statement Determine φ''(x0), φ'''(x0), and φ(4)(x0) for the given point x0 if y=φ(x) is a solution of the given initial value problem. y'' + (sinx)y' + (cosx)y = 0 y(0) = 0; y'(0) = 1 Homework Equations y = φ(x) = Ʃan(x-x0)n The Attempt at a Solution I started off by...
50. ### Series solution, second order diff. eq.

Hi there. I have this differential equation: x^4y''+2x^3y'-y=0 And I have to find one solution of the form: \sum_0^{\infty}a_nx^{-n},x>0 So I have: y(x)=\sum_0^{\infty}a_n x^{-n} y'(x)=\sum_1^{\infty}(-n) a_n x^{-n-1} y''(x)=\sum_2^{\infty}(-n)(-n-1) a_n x^{-n-2} Then, replacing in the diff...