Question

Power series

Find the particular solution of the differential equation: (x^2+1)y"+xy'-4y=0 given the boundary conditions x=0, y=1 and y'=1. Use only the 7th degree term of the solution. Solve for y at x=2. Write your answer in whole number.

Answer #1

1. Find the general solution to the differential equation y''+
xy' + x^2 y = 0 using power series techniques

Solve the following differential equation using taylor series
centered at x=0:
(2+x^2)y''-xy'+4y = 0

Find the power series solution of the differential equation
y"-xy'+6y=0 about the ordinary point x=0

Given the second-order differential equation
y''(x) − xy'(x) + x^2 y(x) = 0
with initial conditions
y(0) = 0, y'(0) = 1.
(a) Write this equation as a system of 2 first order
differential equations.
(b) Approximate its solution by using the forward Euler
method.

Find two solutions of a power series for the differential
equation y'' - xy = 0 surrounding the ordinary point x=0

find the minimum convergence radius of the solutions on power
series of the differential equation (x^2 -2x+10)y''+xy'-4y=0
surrounding the ordinary point x=1

Series Solution Method. Solve the given differential equation by
means of a power series about the given point x0. Find the
recurrence relation; also find the first four terms in each of two
linearly independent solutions (unless the series terminates
sooner). If possible, find the general term in each solution.
(1 − x)y′′ + y = 0, x0 = 0

Find the general solution of the given higher order differential
equation
y^(4) + 4y^(3) − 4y^(2) − 16y^(1) = 0
Derivatives of Y not power

26. Find the solution of the differential equation.
y'' +4y' +4y =0 ; y(-1)=2 and y'(-1)=-1

Find a power series solution of the given differential equation.
Write the solution in terms of power series of familiar elementary
functions.
a. (3? − 1)?′ + 3? = 0
b. ?′ − 10?? = 0

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