question_answer 29)

y = ex (a cos x + sin x)  

Answer:

y = ex (a cos x + b sin x)                                    ?.. (1)       Differential it w.r.t. x, we get             y? = ex (?a sin x + b cos x) + ex       (a cos x + b sin x)             y? = ex (?a sin x + b cos x) + y   ?.. (2)                         [Using (1)]       Again differentiate w.r.t. x       y? = ex ? (?a cos x ? b sin x) + ex                         (?a sin x + b cos x) + y?                         which is the required differential equation.