 Hi and welcome to the session. Let us discuss the following question. Question says, for the following differential equation, find the particular solution satisfying the given condition. Given differential equation is, dy upon dx is equal to y multiplied by tan x. And the given condition is, y is equal to 1 when x is equal to 0. Let us now start with the solution. Now we are given with differential equation, dy upon dx is equal to y tan x. Let us name this equation as 1. Now separating the variables in equation 1, we get dy upon y is equal to tan x dx. Now integrating both the sides of this equation, we get integral of dy upon y is equal to integral of tan x dx. Now using these two formulas of integration, we can find both these integrals. Now this integral is equal to log y and this integral is equal to minus log cos x plus log c, where log c represents the constant of integration. Now using this law of logarithms, we can write right hand side of this equation as log c upon cos x. Now using this law of logarithms, on both sides of this equation, we get y is equal to c upon cos x. Now multiplying both the sides of this equation by cos x, we get y cos x is equal to c. Now the given condition in the question is y is equal to 1 then x is equal to 0. Now to determine c, we will substitute x is equal to 0 and y is equal to 1 in this equation. Let us name this equation as 2. Now substituting y is equal to 1 and x is equal to 0. In equation 2, we get 1 multiplied by cos 0 is equal to c. Now we know cos 0 is equal to 1. So we can write 1 multiplied by 1 is equal to c. Now this further implies c is equal to 1. Now substituting this value of c in equation 2, we get y cos x is equal to 1. Now dividing both sides by cos x, we get y is equal to 1 upon cos x. Now we know 1 upon cos x is equal to sec x. So we can write y is equal to sec x. Now the particular solution of the given differential equation is y is equal to sec x. This is our required answer. This completes the session. Hope you understood the solution. Take care and have a nice day.