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 first four terms in the Taylor series expansion of the
solution to
a. y′(x)=y(x)−x,y(0)=2.
b. y′(x)=2xy(x)−x3,y(0)=1.
c. (1+x)y′(x)=py(x),y(0)=1.
d. y′(x) = ?x2 + y2(x), y(0) = 1.
e. y′′(x)−2xy′(x)+2y(x)=0,y(0)=1,y′(0)=0.
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.