Problem 5: An ordinary differential equation Grading criteria: code correctness for a, mathematical thoughtfulness for b. a. Use scipy.integrate. solve_ivp to numerically solve the differential equation y2 + t2 with the initial condition y(0) = 1, computing at least 25 sample points in the range (including the endpoints). In [ ]: from scipy.integrate import solve_ivp import numpy as np def f(t, y): return t/(y**2 + t**2) integrate.solve_ivpf, (0,1000000), (0,1), t_eval=np.linspace(0, 25, 1000000)) b. Using your answer to a, make a guess about the asymptotic behavior of y ast + oo, and justify your reasoning. Your justification may include a plot, made using matplotlib.pyplot. (If y prefer, you may derive an exact formula for y and read off the asymptotic behavior that way.) In [ ]: #compute the diff eqn and the eqn you get is the one you can plot and then just read the asymtotes Problem 5: An ordinary differential equation Grading criteria: code correctness for a, mathematical thoughtfulness for b. a. Use scipy.integrate. solve_ivp to numerically solve the differential equation y2 + t2 with the initial condition y(0) = 1, computing at least 25 sample points in the range (including the endpoints). In [ ]: from scipy.integrate import solve_ivp import numpy as np def f(t, y): return t/(y**2 + t**2) integrate.solve_ivpf, (0,1000000), (0,1), t_eval=np.linspace(0, 25, 1000000)) b. Using your answer to a, make a guess about the asymptotic behavior of y ast + oo, and justify your reasoning. Your justification may include a plot, made using matplotlib.pyplot. (If y prefer, you may derive an exact formula for y and read off the asymptotic behavior that way.) In [ ]: #compute the diff eqn and the eqn you get is the one you can plot and then just read the asymtotes