 Welcome to the session, I am Deepika here. Let's discuss the question which says, find the general solution of the following differential equation, x plus y into dy by dx is equal to 1. Let us first understand, how to find the general solution of the differential equation of the form dx by dy plus p1y is equal to q1. Now this is a first order linear differential equation here, p1 and q1 are constants or functions of y only. Now the integrating factor is given by e raised to the power p1dy and the solution of the given differential equation is given by x into integrating factor is equal to integral of q1 into integrating factor dy plus c. So this is a key idea behind our question. We will take the help of this key idea to solve the above question. So let's start the solution. Now the given differential equation is x plus y into dy by dx is equal to 1 or this can be written as dx by dy is equal to x plus 5. Again it can be written as dx by dy minus x is equal to 5. Let us give this equation as number 1. Now according to our key idea, this is a linear differential equation of the form dx by dy plus p1x is equal to q1. Here p1 is equal to minus 1. Therefore integrating factor is equal to e raised to the power minus 1 dy. This is equal to e raised to the power minus 5. Now on multiplying both sides of equation 1 by the integrating factor e raised to the power minus y we get e raised to the power minus y into dx by dy minus x into e raised to the power minus y is equal to y into e raised to the power minus 5. Now left hand side of this equation can be written as d by dy of x into e raised to the power minus y is equal to y into e raised to the power minus 5. Now integrating both sides with respect to y we have integral of d by dy of x into e raised to the power minus y. dy is equal to integral of y into e raised to the power minus y dy. Now this can be written as x into e raised to the power minus y is equal to i plus c where i is equal to integral of y into e raised to the power minus y dy. Let us give this equation as number 2. Now we will integrate this by parts. So we have i is equal to y into integral of e raised to the power minus y dy minus integral of d by dy of y into integral of e raised to the power minus y dy and this is equal to y into minus e raised to the power minus y plus integral of e raised to the power minus y dy. Again i is equal to minus y into e raised to the power minus y minus e raised to the power minus y on substituting the value of i in equation 2 we have. Therefore from equation 2 we have x into e raised to the power minus y is equal to minus y into e raised to the power minus y minus e raised to the power minus y plus c. Now on multiplying each term of the above equation by e raised to the power y we get x is equal to minus y minus 1 plus c into e raised to the power y or x plus y plus 1 is equal to c into e raised to the power y. Hence the general solution of the given differential equation is x plus y plus 1 is equal to c into e raised to the power 5. So this is our answer for the above question. I hope the solution is clear to you and you have enjoyed the session. Bye and take care.