This question requires a code in MatLab. Please answer the question in Matlab! If you do not have Matlab or can not answer the ENTIRE question, then please do not answer.

6. This question uses MATLAB. The differential equation dxdy=yx+x2+y2 describes the shape of a plane curve C that will reflect all incoming light beams to the same point and could be a model for a mirror of a reflecting telescope, a satellite antenna, or a solar collector. Solve this differential equation as follows. (a) Verify that the differential equation is homogeneous. Show that the substitution y=ux leads to 1+u2(11+u2)udu=xdx Use the substitution w=11+u2 and solve the resulting DE to find w=w(x). Then utilize it to find the solution of the differential equation (1). Show that the curve C is a parabola with focus at the origin and is symmetric with respect to the x-axis. (b) Verify your answer for (a) by using the following commands to solve the differential equation (1). Provide the solutions with real values given by MATLAB. clear all; \% clear the workspace syms y(x)% create symbolic variables x and y(x) eqn =diff(y,x)==(x+sqrt(x2+y2))/y;% define the differential equation GenSol (x)= dsolve(eqn) \% solve for the general solution