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Please answer all parts of the question. Please show all work and all steps. 1a.) Show that...

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Advance Math

Please answer all parts of the question. Please show all workand all steps.

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

1b.) Find the value of a such that the existence and uniquenesstheorem applies to the ivp x' = (3/2)((|x|)^(1/3)), x(0) = a.

1c.) Find the limits, as t approaches both positive infinity andnegative infinity, of the solution Φ(t) of the ivp x' =(x+2)(1-x^4), x(0) = 0

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