Solving Differential Equations and Calculating Volume of Spherical Tank in MATLAB

Solve Differential Equation using Ode45 Solver

Q.1Solve the following differential equation in MATLABusing solver ‘ode45’dy/dt = 2t Solve this equation for the time interval [0 10] with a step size of 0.2 and the initial condition is 0. Q.2 Solve this system of equationsusing Gauss Elimination in MATLABby writing a Function file.10y + z = 2x + 3y –z = 6 2x + 4y + z = 5 Q.3 Consider the function f(x)= x3–2x + 4 on the interval [-2, 2] with h=0.25. Write the MATLAB function fileto find the first derivatives in the entire interval by all three methods i.e., forward, backward, and centered finite difference approximations. Q.4You are designing a spherical tank to hold water for a small village in a developing country. The volume of liquid it can hold can be computed asfollows: 2[3]3RhVh?−=Where V=volume [m3], h=depth of water in tank [m], and R= the tank radius [m].If R=3m, what depth must the tank be filled to so that it holds 30 m3? Write a function file to solve for the depth of the tank using three iterations of the False-PositionMethod.