Practice Topic 1: Guessing Solutions


Part a: Finding all solutions


For each differential equation below, find either a single function or parameterized family of functions that solves the equation and satisfies all of the given initial conditions.

In each equation, yy is a function of tt that you are solving for.

Please enter any multiplication explicitly with * symbols so the parcer can understand your answer, like this:

2t3e5t2⟶2∗t3∗e(5∗t2).2t^3e^{5t^2} \longrightarrow 2*t^3*e^{(5*t^2)}.

Problem 1

Find a family of functions that solves the equation and satisfies the conditions below.

y′′=0y'' = 0

Initial Conditions to Check:

  • ⬜️y(0) = 0 and y'(0) = 0
  • ⬜️y(0) = 1 and y'(0) = 1
  • ⬜️y(0) = 2 and y'(0) = 0