Show that ϕ(t) = e2t is a solution of y′ − 2y = 0 and that y = cϕ(t) is also a solution of this equation for any value of the constant c. b.Show that ϕ(t) = 1/t is a solution of y′ + y2 = 0 for t > 0, but that y = cϕ(t) is not a solution of this equation unless c = 0 or c = 1. Note that the equation of part b is nonlinear, while that of part a is linear.

Question

Show that ϕ(t) = e2t is a solution of y − 2y = 0 and that y = (t) is also a solution of this equation for any value of the constant c.

b.Show that ϕ(t) = 1/t is a solution of y + y2 = 0 for t > 0, but that y = (t) is not a solution of this equation unless c = 0 or c = 1. Note that the equation of part b is nonlinear, while that of part a is linear.

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