Question

Calculus

Alan, Betty and Catherine had to find a solution of the differential equation

\frac{d y}{d x}=3 x^{2}(y-4)

After much discussion,

\text { Alan said: } y(x)=2 e^{x}+3 \text {, }

\text { Betty said: } y(x)=e^{x^{3}}+4, \text { and }

\text { Catherine said: } v(x)=4 \text {. }

(a) Who is right? Justify your answer by taking derivatives.

(b) Which of the functions suggested by Alan, Betty and Catherine satisfies the differential equation and the initial condition: y(0) = 5?


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