 Hi and welcome to the session. Let's work out the following question. The question says solve the following differential equation that is cos square x into dy by dx plus y is equal to tan x. Let us see the solution to this question. We have cos square x into dy by dx plus y is equal to tan x. Now dividing both the sides by cos square x we get dy by dx plus secant square x into y is equal to tan x into secant square x. Therefore integrating factor is equal to e raise to the power integral of secant square x dx that is equal to e to the power tan x. Now we see that this is the first order differential equation. Therefore solution is given by y into integrating factor is equal to integral of integrating factor multiplied by tan x into secant square x dx plus a constant c. This implies y into e raise to the power tan x is equal to integral e raise to the power tan x into tan x secant square x dx plus c. We put tan x to be equal to t. This implies secant square x dx is equal to dt. Therefore y into e raise to the power t is equal to integral t into e raise to the power t dt plus the constant c. Now we integrate this by parts. So we have t into integral e raise to the power t dt minus integral derivative with respect to t of t that is 1 into integral e raise to the power t dt into dt plus the constant c. This is equal to t into e raise to the power t minus integral e raise to the power t dt plus the constant c. This is equal to t into e raise to the power t minus e raise to the power t plus the constant c. Therefore y into e raise to the power tan x is equal to e raise to the power tan x into tan x minus 1 plus the constant c. So this is our answer to this question. I hope that you understood the solution and enjoyed the session. Have a good day.