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 infinite series solution about x = 0 for the following
differential equation x2y"+ 4xy' + (2+x)y = 0,without using k
substitution and using Bessel's, Legrende's, or frobenius
equations.
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 the following differential equation:
x2y"-2xy'+(x2+2)y=0
Given that y1=x cos x is a solution, find a second
linearly independent solution to the differential equation.
Write the general solution.
Consider the equation y''− (sin x)y = 0.
Find the general solution as a power series centered at x = 0.
Write the first six nonzero terms of the solution. Write the two
linearly independent solutions that form the general solution.
Differential Equations
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.