 Hi and welcome to the session. I am Shashi and I am going to help you with the following question. Question says, find the general solution for the following differential equation. Given differential equation is dy upon dx is equal to sin inverse x. Let us now start with the solution. Now the given differential equation is dy upon dx is equal to sin inverse x. Now this further implies dy is equal to sin inverse x dx. Now integrating both the sides of this equation we get integral of dy is equal to integral of sin inverse x dx. Now first of all we will find out this integral. Let us assume that i is equal to integral of sin inverse x dx. Now put sin inverse x is equal to t. This implies x is equal to sin t. Now differentiating both the sides with respect to x we get dx is equal to cos t dt. Now substituting t for sin inverse x and cos t dt for dx in this integral we get i is equal to integral of t cos t dt. Now we can find this integral by using the method of integration by parts. Now let us take t as a first function and cos t as a second function. Now applying integration by parts we get i is equal to first function that is t multiplied by integral of second function that is cos t dt. Minus integral of derivative of t or we can say derivative of first function multiplied by integral of second function with respect to t only. Now using this formula of integration we get this integral is equal to sin t. So here we can write t sin t minus integral of derivative of t with respect to t is 1 and this integral is equal to sin t and we will write this dt as it is. Now we can find this integral by using this formula of integration. So this integral is equal to minus cos t so we can write t sin t minus minus cos t plus c where c is the constant of integration. Now we know t is equal to sin inverse x. Now substituting sin inverse x for t in this term we get x multiplied by sin inverse x. Now minus m minus sin will get multiplied and we will get a plus sign. Now we know sin t is equal to x. So we can write cos t is equal to square root of 1 minus sin square t. Now substituting x for sin square t in this expression we get cos t is equal to square root of 1 minus x square. So here we can write square root of 1 minus x square for cos t and we will write this constant of integration c as it is. Now let us name this expression as 1. Now we will substitute this value of i in expression 1. So here we can write substituting value of i in 1 we get integral of dy is equal to x sin inverse x plus square root of 1 minus x square plus c. Now using this formula of integration we get integral of dy is equal to y. So we can write y is equal to x sin inverse x plus square root of 1 minus x square plus c. So the required solution of the given differential equation is y is equal to x sin inverse x plus square root of 1 minus x square plus c. This completes the session. Hope you understood the solution. Take care and keep smiling.