Find at least the first four nonzero terms in a power series expansion about co = 0 for the general solution to the given differential equation y"+y=0. page 2

Step-by-step explanation:

Given is a differential equation

SInce it is a power series solution let us assume

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Find I and II derivative

Now substitute in the given DE

2a_2 +3(2)a_3x^2+...+a_n n(n-1)x^{n-2} +... a_0+a_1x+....+a_nx^n +....=0\\\\a_{n-2} +n(n-1) a_n =0\\a_n = \frac{-a_{n-2}}{n(n-1)

Thus the solution is a power series with recurring formula

a_n = \frac{-a_{n-2}}{n(n-1)

the right system of equations to describe the situation would

be on the form:

x1 = 8000 + y1*t

and

x2 = 8000 + y2*t

where x1 and x2 represents the total money of imogene and her

friend respectively at the end of t years.

now for the value of amount earned, y1 and y2:

y1=8000*0.08

y2=2000*√(t-2)

arrange the equations with like terms in columns.

analyze the coefficients of x or y.

add the equations and solve for the remaining variable.

substitute the value into either equation and solve.

check the solution.

step-by-step explanation: