Use sympy to solve the following problems: (a) Solve u'(t) + \frac{1}{t} u(t) = e^tu′(t)+t1u(t)=et subject to u(1) = 3.u(1)=3. (b) Find the family of functions that satisfies P''(s) = 3\, P'(s) - 2\, P(s)P′′(s)=3P′(s)−2P(s). In other words, find the general solution to the differential equation. Hint
Before working on this problem, review the file demo3.pdf on OWL (under the Assignment Info tab). You should also review Week 5 Course Content that discusses sympy.
Your solution to each part below must clearly correspond to the python code you have written. It is your responsibility to make the connection clear to the grader. If it is not clear, then marks will be deducted.
Use sympy to solve the following problems:
(a) Solve u'(t) + \frac{1}{t} u(t) = e^tu′(t)+t1u(t)=et subject to u(1) = 3.u(1)=3.
(b) Find the family of functions that satisfies P''(s) = 3\, P'(s) - 2\, P(s)P′′(s)=3P′(s)−2P(s). In other words, find the general solution to the differential equation. Hint: the number ee is understood by sympy as either sympy.E or sympy.exp(1).
(c) Solve the differential equation in part (b) subject to P(1) = -1P(1)=−1 and P'(e) = 1P′(e)=1.
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