7. For supersonic flow, the linearized perturbation velocity equation is written as 2x22^y22^=0, where ^ is the perturbed velocity potential, =M21 and M is the free stream Mach number. (a) Show that a solution to this equation is the functional ^=f(xy); (b) Derive the relationship between the perturbed velocity components u^ and v^; (c) With the linearized pressure coefficient, derive Cp=2, where is angle between the tangent to the surface and the freestream; (d) Calculate the lift and drag coefficients for a flat plate at angle of attack =2.0 and Ma=3.0(15)