Question

Differential Equations: Find the general solution by using infinite series centered at a.

1.y′′ − xy′ − y = 0, a = 0.

Answer #1

Solved using power series method

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 general solution to the equations:
1)y'=x-1-y²+xy²
2)xy²dy=(x³+y³)dx

xy'-4y=0, find an infinite series solution.

Find a power series solution for the differential equation,
centered at the given ordinary point: (a) (1-x)y" + y = 0, about
x=0
Please explain final solution and how to summarize the recursive
relationship using large pi product (i.e. j=1 to n)

Use a series centered at x0=0 to find the general solution of
y"+x^2y'-2y=0. Use a series centered at x0=0 to find the general
solution. Write out at least 4 nonzero terms of each series
corresponding to the two linearly independent solutions.

1. Find the general solution of each of the following
differential equations a.) y' − 4y = e^(2x) b.) dy/dx = 1/[x(y −
1)] c.) 2y'' − 5y' − 3y = 0

Find the solution of the nonlinear differential equation in
terms of an infinite power series and derive a formula for the
coefficients of the power series expansion for y(x).
y'' - x*y = 0

y'''' - y'' = x2 + sinx
Find the general solution.
(Differential Equations)

3. Find the general solution to each of the following
differential equations.
(a) y'' - 3y' + 2y = 0
(b) y'' - 10y' = 0
(c) y'' + y' - y = 0
(d) y'' + 2y' + y = 0

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