 I am welcome to our session. Let us discuss the following question. The question says solve x squared into dy by dx plus y squared equals to xy into dy by dx given that value of y is 1 when x is equal to 1. Let's now begin with the solution. Given differential equation is x squared into dy by dx plus y squared equals to xy into dy by dx. Now this implies x squared minus xy into dy by dx is equal to minus y squared. This implies dy by dx is equal to minus y squared divided by x squared minus xy. This implies dy by dx is equal to y squared by xy minus x squared. Now this is a homogeneous differential equation. So we will put y as v into x. Now differentiating this equation with respect to x, we get dy by dx equals to v plus x into dv by dx. Now substituting vx in place of y and v plus x into dv by dx in place of dy by dx, we get v plus x into dv by dx equals to v squared x squared divided by x into vx minus x squared. This implies v plus x into dv by dx is equal to v squared x squared divided by vx squared minus x squared. This implies v plus x into dv by dx is equal to v squared by v minus y. This implies x into dv by dx is equal to v squared by v minus 1 minus v. This implies x into dv by dx is equal to v squared minus v squared plus v divided by v minus 1. This implies x into dv by dx is equal to v by v minus 1. This implies v minus 1 by v into dv is equal to 1 by x into dx. This implies 1 by v, sorry, 1 minus 1 by v into dv is equal to 1 by x dx. Now integrating both sides, we get integral dv minus integral 1 by v dv equals to integral 1 by x dx. Now integral dv is equal to v. Integral 1 by v dv is equal to log mod v. Integral 1 by x dx is equal to log mod x plus c. Now y is equal to vx. This implies y by x is equal to v. So we have y by x minus log mod y by x equals to log mod x plus c. This implies y by x is equal to log mod y by x plus log mod x plus c. This implies y by x is equal to log mod y minus log mod x plus log mod x plus c. This implies y by x is equal to log mod y plus c. Given that value of y is equal to 1 when x is equal to 1, so we are now going to put x equals to 1 and y equals to 1 in the equation y by x equals to log mod y plus c. So we have 1 equals to log 1 plus c. This implies c is equal to 1. By substituting the value of c, we get y by x equals to log mod y plus 1. The inside required solution is y by x equals to log mod y plus c. This is our required answer. So this completes the session. Bye and take care.