Question $6$

$15$ pts

In this question, we will consider the numerical approaches for Ordinary Differential Equations $($ODEs$).$ Please refer to the codes provided in the module on CANVAS.

Consider the following:

$\frac{dy}{dx}=3xy$

Providing evidence of your approach in a spreadsheet or word document, for Euler's method and $\frac{2^{nd}}{4^{th}}$ Order Runge$-$Kutta methods, obtain the solution of this ODE for $)=(2$ where $)=(1(4$dp$).$ Consider the number of steps $n$ of $n=250,500$ and $750.$

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