 Hello and welcome to the session. The given question says verify that y is equal to a cos x minus b sin x is a solution of the differential equation d square y divided by dx square plus y is equal to 0. Let's start with the solution. So here we are given that y is equal to a cos x minus b sin x. So here we shall first find the second derivative of y and then we shall add it to the given y and show that it is equal to 0. So first let us find its first derivative which is given by dy divided by dx so this is equal to minus a sin x minus b cos x and its second derivative is equal to minus a cos x since derivative of sin x is cos x minus b and derivative of cos x is minus sin x and this is equal to minus a cos x plus b sin x or this can also be written as taking minus sin common a cos x minus b sin x therefore we have d square y divided by dx square is equal to minus of and this function is given to us as y or before we have d square y divided by dx square plus y is equal to 0. This is what we are required to prove. This completes the session. Bye and take care.