Question: Consider the solution of the differential equation \(y^{\prime}=y\) passing through \(y(0)=1\).

a.) Sketch the slope field for this differential equation, and sketch the solution passing through the point \((0,1)\).

b.) Use Euler's method with step size \(\Delta x=0.1\) to estimate

the solution at \(x=0.1,0.2, \ldots, 1\).

c.) Plot the estimated solution on the slope field; compare

the solution and the slope field.

d.) Check that \(y=e^{x}\) is the solution of \({{y}^{\prime }}=y\) with \(y(0)=1\).

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