Find the first four nonzero terms in a power series expansion of the solution to the given initial value problem. 2y''-6( cos x)y' -6y=0; y y(x)= 3+2 x- +2√x - T 3 + 2 2 X T (7) = 3, 2 - 2 2 + 2 1 3 = 3, y' X T 3 (2) +. = 2 2 (Type an expression that includes all terms up to order 4. Type an exact answer, using as needed.)

2,5) Please type answer or make it very easy to read

2. (a) Consider the DE y"+ 4x²y' = 0. Explain what makes x = 0 an ordinary point. (b) Assume a series solution y=Σcx" about the ordinary point x= 0. Show all the n=0 work needed to find the recursive formula for the coefficients. Cn.

A company decides to change its floor plan from cubicle to open office. This will bring in a constant stream of $1,000 in extra income annually. If the company invests this extra income in an account that earns 2.5% continuously compounded interest for ten years, is it worth the change? The change in floor plan costs $7,000.

Try to use the method of Frobenius to find a series expansion about the irregular singular point x = 0 for a solution to the given differential equation. If the method works, give the first four nonzero terms in the expansion. If the method does not work, explain what went wrong. x²y' + (3x-4)y' + y = 0

Try to use the method of Frobenius to find a series expansion about the irregular singular point x = 0 for a solution to the given differential equation. If the method works, give the first four nonzero terms in the expansion. If the method does not work, explain what went wrong. 3x²y+3y' - 6y=0