1.7. Modify the Euler code of Example 1.6 to numerically solve and plot five different realizations of the solutions of the following SDEs:

1. dX =



2X 1+t +(1+t)2



dt+(1+t)2dW with X0 = 0 and X0 = 1 ;

2. dX = dt+2

√

XdW with X0 = 1 ;

3. dX=−12 e−2Xdt+e−XdW with X0 = 0 ;

4. dX =



12 X+



1+X2



dt+



1+X2dW with X0 = 0 ;

5. dZ = Z3dt−Z2dW with Z(0) = 1 .