5.5. Determine a partial sum of the series solution about t = 0 to x+3 (t²+1)x+x=0, where x(0) = 1 and x(0) = −1. Compare your partial sum approximations to a solution determined numerically.
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- Express the function as the sum of a power series by first using partial fractions. f(x) = 8 x2 − 2x − 15Q4. Differentiate term by term the power series =(x-7)". Q5. Solve: = y²(1 + x²), y(0) = 1. dx5.4. Determine a partial sum of the series solution about t = 0 to x− (t+1)x+t²x=0, where x(0) = 1 and x(0) = 1. Compare your partial sum approximations to a solution determined numerically.
- Express the function as the sum of a power series by first using partial fractions. (Give your power series representation centered at x = 0.) 9. f(x) x2 - 3x 18 f(x) n = 0Assume the solution of = 5 – y, y(0) = 2 can be written in the form of a power series, y = E-o Cnx". dt Determine the first three nonzero coefficients co, C1, and c2. Then you have a second-degree polynomial that approximates the true solution of the initial value problem. Use your second-degree polynomial to estimate У(1).Find the first five nonzero terms of a power series solution about t=0 for the ODE y''+ty=0. Simplify the coefficients completely.
- Express the function f(x) = k/(1+bx)^2 in power series form. then evaluate the series at x = 0.048 using the first few terms (from m = 0 to m = 5 ) of the series if k = 17.8 and b = 2. Round off the final answer to five decimal placesFind the first 4 terms of the power series solution to e" y" + xy = 0, y(0) = 1, y'(0) = -1.Let f(x) = 1 + x 1 X Find the power series representation for the function f(x) by completing the following steps: a. First, express the fraction 1¹ as a power series. = X b. Now, express the fraction as a power series. 1-x 1+x x c. The function f(x) 1-x 1-x + 1 is the sum of the two series from parts (a) and (b). Express the function f(x) as a power series. d. What is the interval of convergence and the radius of convergence for this power series?
- Express the function f (x) = k ln (1 + cx) in power series form. Then, evaluate the series at x = 0.083 using the first six terms of the series if k = 18.98 and c = 6. Round off the final answer to five decimal places.Consider the equation y' = (x + 1)y. Assume a power series solution : y(x) = a0 + alx + a2x^2 + a3x^3. Find a1, a2 and a3 in terms of a0.Find the series solution about the ordinary point x=0 (1-x2)y''-2xy'+2y=0