I need help with my math homework, please

C File | C:/Users/jackl/Do... to G of 1 Q + . .. Due date: 11.59pm, February 28th, 2022 (1) (6 points total) Consider the following differential equation, with time domain t E (0, 1): Sy' = (12 - 1)y, ly(0) = 1. Solve it with: (a) (1 points) Euler's method, with step size h = 0.25. Find also the upper bounds for the local and global truncation errors. (b) (1 points) Midpoint method, with step size h = 0.2. (c) (2 points) Heun's method, with no recursion (i.e. m = 1), and step size h = 0.25. (d) (2 points) Runge-Kutta of order 4, and step-size h = 0.25. (2) (4 points total) Consider the following system of differential equation, with time domain t E (0, 1): x' = -2x+ 4e-*, y' = -xy213, I(0) = 2, y(0) = 4. (a) (2 points) Euler's method, with step size h = 0.25. Find also the upper bounds for the local and global truncation errors. (b) (2 points) Runge-Kutta of order 4, and step size h = 0.25. (3) (5 points) The chemical reaction from solution A to B takes into two steps. The governing equations are: dt =T-1(CAo - CA1) - kCA1, dCB dt = -T"ICB, + kCA1, dC A2 dt =T"(CA] - CA2) - kCA2, dCB2 dt =T-1(CB1 -CB2) + kCA2, where CAo = concentration of A at the inlet of the first reactor, CA1 = concentration of A at the outlet of the first reactor (and inlet of the second), CA2 = concentration of A at the outlet of the second reactor, CB1 = concentration of B at the outlet of the first reactor (and inlet of the second), CB2 = concentration of B outlet of the second reactor. Use k = 0.12, time domain te (0, 1), h = 1/4, 7 - 1/5. Assume that, at the starting time, CAo - 20, and all other dependent variables are zero. Solve with Euler's method. O