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CalculusQ&A LibraryShow 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.Start your trial now! First week only $4.99!*arrow_forward*

Question

Show that *ϕ*(*t*) = *e*^{2t} is a solution of *y*^{′} − 2*y* = 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*^{′} + *y*^{2} = 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.

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