 Hi and welcome to the session. I am Shashri 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 e raised to the power x plus e raised to the power minus x dy minus e raised to the power x minus e raised to the power minus x dx is equal to 0. Let us now start with the solution. Now the given differential equation is e raised to the power x plus e raised to the power minus x multiplied by dy minus e raised to the power x minus e raised to the power minus x multiplied by dx is equal to 0. Now adding this term on both the sides of this equation we get e raised to the power x plus e raised to the power minus x dy is equal to e raised to the power x minus e raised to the power minus x dx. Now separating the variables of this equation we get dy is equal to e raised to the power x minus e raised to the power minus x upon e raised to the power x plus e raised to the power minus x dx. Now integrating both sides of this equation we get integral of dy is equal to integral of e raised to the power x minus e raised to the power minus x dx upon e raised to the power x plus e raised to the power minus x. Now first of all we will find out this integral. Now clearly we can see in this integral derivative of denominator is numerator. So we will find this integral by substitution method. Now we can write put e raised to the power x plus e raised to the power minus x is equal to t. Now differentiating both sides with respect to x we get e raised to the power x minus e raised to the power minus x is equal to dt upon dx. Now this further implies e raised to the power x minus e raised to the power minus x dx is equal to dt. Now we can write this integral is equal to integral of dt upon t. Clearly we can see we can substitute t for denominator here and dt for numerator here and we get this integral as integral of dt upon t. Now using this formula of integration we get this integral is equal to log of t plus c1 where c1 is the constant of integration. Now we will substitute e raised to the power x plus e raised to the power minus x for t here and we get log of e raised to the power x plus e raised to the power minus x plus c1. So we get this integral is equal to log of e raised to the power x plus e raised to the power minus x plus c1. Now let us name this expression as 1 and this expression as 2. Now we will substitute value of this integral from expression 2 in expression 1. We get integral of dy is equal to log of e raised to the power x plus e raised to the power minus x plus c1. Now using this formula of integration we get integral of dy is equal to y plus c2 where c2 is the constant of integration and y plus c2 is equal to log of e raised to the power x plus e raised to the power minus x plus c1. Now this further implies y is equal to log of e raised to the power x plus e raised to the power minus x plus c1 minus c2. Now substituting c for c1 minus c2 in this equation we get y is equal to log of e raised to the power x plus e raised to the power minus x plus c. So the required solution of the given differential equation is y is equal to log of e raised to the power x plus e raised to the power minus x plus c. So this is our required answer. This completes the session. Hope you understood the solution. Take care and have a nice day.