Problem #5: Consider the differential equation (6x + 2xy) = 5x + 6x + 21¹ Problem #5(a): Problem = 5(b): (a) For which value of n is the first-order (nonlinear) differential equation above homogeneous. (b) For the value of n found in part (a), use the method of homogeneous equation to find in explicit form the unique solution of the differential equation above that satisfies the initial condition y(1) = -6. Enter your answer as a symbolic function of x, as in these examples 4

II. Rewrite the following second order differential equations as a system of first-order equations: (a) u" + 3u' +5u = 0 (b) u" + 6u' +9u = sin(2t)

Find the general solution of the given second -order differential equations. (2) (a) 2y +29 +y =0 (6)

Specifically a differential equations problem. Question in pic below.