Please show all work and give explanation for question 1-3, thank you very much

1. Find the differential equation which describes the family of curves y? = c1 (I + 1). 2. Classify the following differential equations as linear or non-linear. Give the order of each and state whether each is separable, homogeneous of degree k, exact, etc. (a) y' = y' - 4 (b) (costsinx - ry?) dr + y(1 - r?) dy = 0 (c) dy _ 3xy = 0 (d) 2x'y dr + (x* + y' ) dy = 0 (e) y = my' t - (y')2 3. Solve the following differential equations subject to the given initial conditions: y dy x dx In y y(1) = 1; (b) ryy' = 3y' + x2, y(-1) = 2; (c) (x2 + 4)-2 = 2x - 8ry, y(0) = -1. 4. Determine the orthogonal trajectories of the given family of curves: (a) city? = 1 (b) y = cle z (c) y = 1+ CI 5. Determine whether the given functions are linearly independent or dependent on (-00, 00). (a) fi(t) = 1, f2(x) == 12, f3(1) = 4x - 312; (b) fi(I) = 12, f2(I) = xz; (c) fi(x) = ez, f2(x) = e-z, fa(r) = e47