 Hi, I am welcome to the session. I am Deepika here. Let's discuss the question which says Find the general solution of the following differential equation Y dx plus x minus y square into dy is equal to 0 Let's start the solution. Now the given differential equation is Y dx plus x minus y square into dy is equal to 0 or This can be written as y into dx over dy plus x minus y square is equal to 0 or This can be written as dx over dy plus x over y is equal to y square over y that is what Let us give this equation as number one Now this is a linear differential equation of the form dx by dy plus p1x is equal to q1 here p1 is equal to 1 over y Therefore the integrating factor which is given by e raised to power integral of p1 dy is equal to e raised to power integral of 1 over y dy and this is again equal to e raised to power log y and this is equal to y Now on multiplying both sides of equation one by integrating factor which is equal to y we get y into dx by dy plus x over y into y is equal to y into y or y into dx by dy plus x is equal to y square or this can be written as dy dy of xy is equal to y square on integrating both sides with respect to y we have integral of dy dy of xy into dy is equal to integral of y square dy or this can be written as xy is equal to yq over 3 plus c or x is equal to y square over 3 plus over y the general solution of the given differential equation is x is equal to y square over 3 plus c over y 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 have a nice day