Use a CAS and the concept of level curves to plot representative graphs of members of the family of solutions of the differential equation.

Use a CAS and the concept of level curves to plot representative graphs of
members of the family of solutions of the differential equation.

Use a CAS and the concept of level curves to plot representative graphs of
members of the family of solutions of the differential equation
$\frac{dy}{dx}= \frac{8x + 5}{3y^2 + 1}$. . Which after integrating gives:
$y^3+y = 4x^2+5x +c$
$y^3+y - 4x^2-5x =c$
$\hspace{400pt}$ $\:$Experiment with different numbers of level curves as
well as various rectangular regions defined by a$\leqslant$ x $\leqslant$
b and c $\leqslant$ y $\leqslant$ d. (b) On separate coordinate axes plot
the graphs of the particular solutions corresponding to the initial
conditions: y(0) = −1; y(0) = 2; y(−1) = 4; y(−1) =
−3./p pI have tried plotting the level curves with wolfram
Mathematica as given below. img src=http://i.stack.imgur.com/IJySn.jpg
alt=enter image description here Ineed some help in verifying my answer./p