In: Advanced Math

Find a power series solution of this ODE:

y''+x^2y'=0 ; y(0)=1 y'(0)= 2

Find the general power series solution to the following ode:
y"-4xy'+(4x2-2)y=0

find a power series solution
(x-1)y''+y'=0

Find the general power series solution for the differential
equation
2x^2y''-xy'+(x^2 +1) y =0 about x=0
(Answer should be given to the x^4+r term)

Find the general solution to the ODE y'' − y'/x − 4x^2y = x^2
sinh(x^2)

1)Find the power series solution for the equation y'' − y =
x
2)Find the power series solution for the equation y'' + (sinx)y
= x; y(0) = 0; y'(0) = 1
Provide the recurrence relation for the coefficients and derive
at least 3 non-zero terms of the solution.

x*y' '+y'-x*y=0
1> use Frobenious series solution to solve the ODE.

Find the power series solution for the equation y'' + (sinx)y =
x; y(0) = 0; y'(0) = 1
Provide the recurrence relation for the coefficients and derive
at least 3 non-zero terms of the solution.

. Consider a Bessel ODE of the form:
x^2y"+xy'+(x^2-1)y=0
What is the general solution to this ODE assuming that the
domain of the problem includes x=0? Why?

Use power series to solve the initial value problem
x^2y''+xy'+x^2y=0, y(0)=1, y'(0)=0

Determine step by step power series solution about x=0
for:
4xy'' + 2y' - y = 0.
note: final answer must be in terms of coshx and
sinhx

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