Solve the following ODE in space using finite difference method based on central differences with error O(h2). Use a five node grid. 4u" u(0) = 0 25u0 (1)=2 Solve analytically and compare the solution values at the nodes.

27.1please complete the code

HW 2_2 The volume of a partially-filled spherical tank can be computed as: V = πα 3 (3R – d); where d is the depth of the water in the tank (m) and R is the radius of the tank (m). Given that R=3m, to what depth must the tank be filled so that it holds 30 m³? Write a PYTHON code & implement the bisection algorithm to answer the question correct to 3 sig figs. Plot to select your own initial guesses. Display the answer in an informative sentence, using formatted printing.

Solve the following differential equation using laplace transform methods. You can use a computer to find the constants for partial decomposition

25.18 The following is an initial-value, second-order differential equation: d²x + (5x) dx + (x + 7) sin (wt) = 0 dt² dt where dx (0) (0) = 1.5 and x(0) = 6 dt Note that w= 1. Decompose the equation into two first-order differential equations. After the decomposition, solve the system from t = 0 to 15 and plot the results of x versus time and dx/dt versus time.

Q6