 Hi, and welcome to the session. Let's work out the following question. The question says solve the differential equation dy by dx plus 1 upon x into y is equal to y cube Let us start with the solution to this question here dy by dx Plus 1 upon x into y is equal to y q is a differential equation We divide both the sides by y cube and we get 1 upon y cube into dy by dx Plus 1 upon x into 1 upon y square is equal to 1 we put 1 upon y square to be equal to t this implies Minus 2 by y cube into dy by dx is Equal to dt by dx this we get by differentiating both the sides with respect to x this implies minus 1 upon 2 dt by dx Plus 1 upon x Into t is equal to 1 this we get from this equation because we see that 1 upon y cube into dy by dx is equal to minus 1 by 2 dt by dx Plus 1 upon x into t is equal to 1 this implies that dt by dx minus 2 upon x Into t is equal to minus 2 this we get by multiplying throughout by minus 2 This is a linear differential equation Here where p is minus 2 by x q is minus 2 therefore integrating factor is e raised to power integral p dx That is equal to e raised to power integral minus 2 upon x dx which is equal to e raised to power minus 2 log x Which is equal to e raised to power? log x raised to power minus 2 that is equal to x raised to power minus 2 or 1 upon x square so the required solution will be t into integrating factor is equal to integral minus 2 into integrating factor dx plus the constant This implies that t into 1 upon x square is equal to integral minus 2 into 1 upon x square dx Plus the constant C which is equal to 2 upon x plus C Now we put back the value of t is 1 by y square so we have 1 upon x square y square is equal to Now we see that this is same as integral Sorry, here we have This to be equal to 2 upon x plus the constant C hence 2 x square or 2 y square plus C x square y square is equal to 1 This we get by multiplying throughout by x square y square So this is our answer to this question. I hope that you understood the solution and enjoyed the session. Have a good day