For each of the following equations, state the order and whether it is linear or nonlinear. if it is linear, determine if it is homogeneous or inhomogeneous. provide reasons.

a. uₜ -uₓₓ + 1 = 0
b. uₜ - uₓₓ + xu = 0
c. uₜ - uₓₓₜ + uuₓ = 0
d. uₜₜ - uₓₓ + x² = 0
e. iuₜ - uₓₓ + u/x = 0
f. uₓ (1+u²ₓ)⁻¹/² + uᵧ (1+u²ᵧ )⁻¹/² = 0
g. uₓ + eʸuᵧ = 0
h. uₜ + uₓₓₓₓ + √1 + u = 0