question_answer 1)

      y = x sin x : xy? = y +         .  

Answer:

Given y = x sin x       Differential it w.r.t. x, we get             y? = x cos x + sin x       Multiply it by x        xy? = x2 cos x + x sin x              [Using (1)]                                                 which is the required differential equation.       Therefore, the given function is the required solution of the differential equation.