 Welcome to our session where we discuss the following question. The question says, all the following differential equation, x q plus y q into dy minus x square y into dx equals to 0. Let us now begin with the solution. How given differential equation is, q plus y q into dy minus x square y into dx equals to 0? This implies, dy by dx is equal to y y x q plus y q. This is a homogeneous differential equation. Differentiating both sides with respect to x, we get dy by dx equals to v plus x into dv by t. So now this equation becomes v plus x into dv by t into y is equal to vx divided by into 1 plus vq. So v plus dv by dx is plus vq. This implies v plus v by v by 1 plus vq minus v minus v to the power 4 divided by 1 plus vq. You will integrate both sides of this equation. Get 1 by v to the power 4, integral 1 by v, integral 1 by x with respect to x. This implies minus 1 by 3 vq plus log v is equal to minus log x. This implies minus 1 by 3 vq plus log v plus log x is equal to c is equal to vx. And this implies v is equal to y by x minus 1 by 3 into y q by x q plus this implies minus x q by 3 vq, sorry, 3 y q. And so our required solution is minus x q divided by 3 y q plus log y equals to c. So this completes this equation by n-tech here.