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Answer all parts of question 1. 1a.) Show that the solutions of x' = arc tan...

Answer all parts of question 1.

1a.) Show that the solutions of x' = arc tan (x) + t cannot have maxima

1b.) Show that the solution x(t) of the Cauchy problem x' = 2 + sin(x), x(0) = 0, cannot vanish for t>0

1c.) Let Φ(t) be the solution of the ivp x' = tx - t^3, x(0) = a^2 with a not equal to 0. Show that Φ has a minimum at t=0.

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