Which of the following ordinary differential equations are l

Which of the following ordinary differential equations are linear? Which are homogeneous?
(a) x +cost = 0
(b) (x)2 + cost = 0
(c) x + (cost)2 = 0
(d) ¨x = tx
(e) ¨x = x2 + 1

Solution

a) x +cost = 0

and c) x + (cost)2 = 0

are linear differential equations as it is of first order and first degree equations

only d part is homgenous as it can be expressed as¨x - tx = 0 and here RHS is equal to zero.