Question

Find the general solution near x = 0 of y'' - xy' + 2y = 0. (Power series, recursive formula problem)

Answer #1

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

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.

Find the general solution to xy''' - 2y'' = 0

Solve for the general solution
x^4y''''+4x^3y'''+3x^2y''-xy'+y=0

given that y1=xcos(lnx)and y2=xsin(lnx)form a fundamental set of
solutions to x^2y''-xy'+2y=0,find general solution to
x^2y''-xy'+2y=xlnx

Consider the following ODE
y'' - xy' +2y = 0
Find the recursion formula using the power series approach to
calculate a1 given that a3 = 7

Given that y=e^x is a solution of the equation (x-1)y''-xy'+y=0,
find the general solution to (x-1)y''-xy'+y=1.

Find a general solution: (dy/dx) = (x+xy^2)/2y

Find the solution of the Differential Equation
X^2y''-xy'+y=x

Compute the general power series solution, centered at x = 0, to
the diﬀerential equation
y'' = 2ty.
(You can express your ﬁnal answer by just giving the recursive
relation between the power series coeﬃcients.)

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