 Hi and welcome to the session, I am Shashik and I am going to help you to solve the following question. Question is if y is equal to 5 multiplied by cos x minus 3 multiplied by sin x, prove that d square y upon dx square plus y is equal to 0. Let us find the solution now, we have given y is equal to 5 cos x minus 3 sin x, now differentiating both sides with respect to x, we get dy upon dx is equal to 5 multiplied by minus sin x minus 3 multiplied by cos x, so we get dy upon dx is equal to minus 5 sin x minus 3 cos x, now again differentiating both sides with respect to x, we get d square y upon dx square is equal to minus 5 cos x minus 3 multiplied by minus sin x or it is equal to minus 5 cos x plus 3 sin x, now it can be further written as minus multiplied by 5 cos x minus 3 sin x, here we can see clearly that 5 cos x minus 3 sin x is equal to y, so we can write d square y upon dx square is equal to minus y or we can say this implies d square y upon dx square plus y is equal to 0, so d square y upon dx square plus y is equal to 0, this is our required answer, hence proved we were required to prove this equation only in this question, so hence proved this completes the session, hope you understood the session, good bye.