Q 1859680514.     For each of the exercises given below, verify that the given function (implicit or explicit) is a solution of the corresponding differential equation.

(i) `y = a e^x + b e^(-x) + x^2` :

`x (d^2y)/(dx^2) + 2 (dy)/(dx) -xy + x^2 - 2 = 0`

(ii) `y = e^x (a cos x + b sin x)`:

`(d^2y)/(dx^2) - 2 (dy)/(dx) +2y = 0`

(iii) `y = x sin 3x` :

`(d^2y)/(dx^2) + 9y - 6 cos^3x = 0`

(iv) `x^2 = 2y^2 log y` :

`(x^2 + y^2 ) (dy)/(dx) - xy = 0`



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