 Hi and welcome to the session. I am Deepika here. Let's start the solution question. If y is equal to e raised to power a cos inverse x and minus 1 is less than equal to x, x is less than equal to 1, show that 1 minus x square into d2y by dx square minus x dy by dx minus a square y is equal to 0. So let's start the solution given y is equal to e raised to power a cos inverse x taking logarithm on both sides. We have log y is equal to a cos inverse x into log e. This is equal to log y is equal to a cos inverse x as log e is equal to 1. Now differentiating both sides with respect to x we have on left hand side we have 1 over y into dy by dx is equal to Now derivative of cos inverse x is equal to minus 1 over under root of 1 minus x square. So this is equal to minus a into under root of 1 minus x square. So this implies dy by dx is equal to minus a y upon under root of 1 minus x square. Let us give this equation as number 1. Again this can be written in the form under root of 1 minus x square into under root of 1 minus x square into dy by dx is equal to minus a y. Now again differentiating both sides with respect to x we have now we will apply the product rule here 1 minus x square into d2y by dx square plus dy by dx into 1 over 2 into under root of 1 minus x square into dy dx of 1 minus x square which is equal to minus a into derivative of y with respect to x is dy by dx. So this is equal to 1 minus x square into d2y by dx square plus dy by dx into 1 over 2 into 1 minus x square into minus 2x is equal to minus a into dy by dx. So on cancellation so this is equal to 1 minus x square d2y by dx square minus x into dy by dx is equal to minus a into 1 minus x square dy by dx. Now substitute value of dy by dx from equation 1. On the right hand side we have 1 minus x square d2y by dx square minus x dy by dx is equal to minus a into 1 minus x square dy by dx. So this is equal to 1 minus x square d2y by dx square minus x dy by dx plus a square y is equal to 0. This is minus a square y is equal to 0. Hence we have proved that if y is equal to e raised to power a cos inverse x and minus 1 is less than equal to x, x is less than equal to 1 then 1 minus x square d2y by dx square minus x dy by dx minus a square y is equal to 0. I hope the question is clear to you. Bye and have a nice day.