In: Advanced Math

Solve the following differential equation using the power series method.

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

Solve the differential equation 2x^2y"-x(x-1)y'-y = 0 using the
Frobenius Method

using series to solve
differential equations
using series to solve
differential equations
1.) y’’-(e^5x)y’+xy=0,y(0)=2,y’(0)=1

Solve differential equation by using undetermined coefficient
method
y^''+9y=x^2e^x+6 , y(0)=1 and y^'(0)=1

Solve the following differential equation using the power series method.
(1+x^2)y''-y'+y=0

Consider the differential equation:
y'(x)+3xy+y^2=0.
y(1)=0. h=0.1
Solve the differential equation to determine y(1.3)
using:
a. Euler Method
b. Second order Taylor series method
c. Second order Runge Kutta method
d. Fourth order Runge-Kutta method
e. Heun’s predictor corrector method
f. Midpoint method

Find two power series solutions of the given differential
equation about the point x=0
(x^2+2) y″+3xy'-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)

2. Find the general solution to the differential equation
x^2y''+ y'+y = 0 using the Method of Frobenius and power series
techniques.

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.

Find the power series solution of the differential equation
using the FROBENIUS METHOD xy"+y'+4xy=0 Show all of the steps.

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