I need help with this in PYTHON syntax. PYTHON syntax please

achy problem for a single differential equation of first order applying on of the methods that automatically controls the error less than e by selecting appropriate step-size embedded Runge-Kutta methods either (1) Runge-Kutta-Fehlberg or (2) Euler and modified Euler methods Analysis of Burden and Faires, Ninth Edition, pp. 296-298, or Sixth Edition, pp. 286-292). Specifications (1) To debug and test the work of your program, you may solve the IVP : , tel + y for t E (0,1) and y(0)-0 with exact solution y(t) te (2) Run the program for two values of TOL: 10-2 and 10- (3) Report the number of steps and the obtainod solution at the end point. Plot the obtained approxi- mate solution in the whole interval. Computational examples solve the following problems (1) In a circuit impressed, voltage E, and resistance R, inductance L, capacitance C in parallel, the current satisfies the differential equation Suppose C 0.3 farad, R 1.4 ohms, L 1.7 henries, and the voltage is given by E(e) e-0.06 t sin(2t-). If i(0) 0, find the current i(t) for 0 t 5 (2) A liquid of low viscosity, such as water, flows from an inverted conical tank with circular orifice at the rate 2 A(r) where r is the radius of the orifice, is the height of the liquid level from the vertex of the cone, and A(z) is the area of the cross section of the tank a units above the orifice. Suppose r 0.1 feet g 32feet/sec2, and the tank has an initial water level of 8 feet and initial volume of 512r/3 cubic feet. Find the time when the tank is emptied (3) The irreversible chemical reaction in which two molecules of solid potassi two molecules of water (H20), and three of the gas sulfur dioxide (SO2), four molecules of solid potassium hydroxide (KOH), and two molecules of solid chrome oxide (Cr20s) can be represented symbolic equation: 2K2Cr20 +2H20 +35- -4KOH + 2Cr2Os molecules of H20 and ns molecules of S are originally available at the beginning of the reaction, the following differential equation atoms of solid sulfur (S) combine to yield three molecules by the stoichiometric +3S02. If n molecules of KCro0+, n2 describes the amount y(t) of KOH after time t: (t) k(n-0.5) (n-0.5y) ns-0.75) where k is the velocity constant of the reaction. If k 6.22. 10-19 how many units of potassium hydroxide will have been formed after two seconds ? My advise for this problem would be to go and introduce dimensionless variable, e.g. Y-yi orY ys and rewrite the problem in this new variable with amended constants. ,n 1000,n-1500, e of the class. There will be