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. Use sympy to solve the following problems:(a) Solve u'(t) + u(t) = e' subject to u(1) = 3.(b) Find the family of functions that satisfies P"(s) = 3 P'(s) – 2 P(s). In other words, findthe general solution to the differential equation. Hint: the number e is understood by sympy aseither sympy.E or sympy.exp(1).(c) Solve the differential equation in part (b) subject to P(1) = -1 and P' (e) = 1.

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Answered: Use sympy to solve the following…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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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).