 Hi and welcome to the session. Let us discuss the following question. Question says, find the equation of the curve passing through the point 0 pi upon 4 whose differential equation is sin x cos y dx plus cos x sin y dy is equal to 0. Let us now start with the solution. Now we are given the differential equation and we are asked to find the equation of the particular curve. Given equation is sin x cos y dx plus cos x sin y dy is equal to 0 or we can say we have to find the particular solution of the given differential equation. Now subtracting this term from both the sides we get sin x cos y dx is equal to minus cos x sin y dy. Now let us name this equation as equation 1. Now separating the variables in equation 1 we get sin x upon minus cos x dx is equal to sin y upon cos y dy. Now this further implies minus tan x dx is equal to tan y dy we know sin theta upon cos theta is equal to tan theta. So here we can write tan x for sin x upon cos x and tan y for sin y upon cos y. Now integrating both the sides of this equation we get minus integral of tan x dx is equal to integral of tan y dy. Now we can write this equation as integral of tan y dy is equal to minus integral of tan x dx. Using this formula of integration we get this integral is equal to log of sec y. We will write this is equal to sin as it is. Here we will write this minus sign and we know integral of tan x dx is equal to log of sec x plus log c where log c represents the constant of integration. Now adding this term on both the sides of this equation we get log of sec y plus log of sec x is equal to log of c. Now applying this law of logarithms in left hand side of this equation we get log of sec y multiplied by sec x is equal to log c. Now applying this law of logarithms on both the sides of this equation we get sec y multiplied by sec x is equal to c. Now we know this curve passes through 0 pi upon 4. This is given in the question. So we will substitute 0 for x and pi upon 4 for y in this equation. Let us name this equation as equation 2. Now substituting x is equal to 0 and y is equal to pi upon 4 in equation 2 we get sec pi upon 4 multiplied by sec 0 is equal to c. Now we know value of sec pi upon 4 is equal to root 2 and value of sec 0 is equal to 1. So we get root 2 multiplied by 1 is equal to c or we can simply write it as c is equal to root 2. Now substituting value of c is equal to root 2 in equation 2 we get sec x multiplied by sec y is equal to root 2. Now dividing both the sides of this equation my sec x we get sec y is equal to root 2 upon sec x. Now taking reciprocal on both the sides we get 1 upon sec y is equal to sec x upon root 2. Now we know reciprocal of sec y is cos y. So we can write cos y is equal to sec x upon root 2. So this is the required equation of the curve. This completes the session. Hope you understood the solution. Take care and keep smiling.