 Hi and welcome to the session. Let us discuss the following question. Question says find the general solution of the following differential equation. Given differential equation is x raised to the power 5 dy upon dx is equal to minus y raised to the power 5. Let us now start with the solution. Now the given differential equation is x raised to the power 5 dy upon dx is equal to minus y raised to the power 5. Now let us name this equation as equation 1. Now separating the variables in equation 1 we get dy upon y raised to the power 5 is equal to minus dx upon x raised to the power 5. Now integrating both the sides of this equation we get integral of dy upon y raised to the power 5 is equal to minus integral of dx upon x raised to the power 5. Now we know 1 upon y raised to the power 5 is equal to y raised to the power minus 5. So we can write this integral as y raised to the power minus 5 dy. Similarly here we can write minus integral of x raised to the power minus 5 dx. Now using this formula of integration we can find both these integrals. So here we can write y raised to the power minus 5 plus 1 upon minus 5 plus 1 is equal to minus x raised to the power minus 5 plus 1 upon minus 5 plus 1. plus c1. Here c1 is the constant of integration. Now this further implies y raised to the power minus 4 upon minus 4 is equal to minus x raised to the power minus 4 upon minus 4 plus c1. Now adding x raised to the power minus 4 upon minus 4 on both the sides of this equation we get y raised to the power minus 4 upon minus 4 plus x raised to the power minus 4 upon minus 4 is equal to c1. Now adding these two terms by taking their LCM we get y raised to the power minus 4 plus x raised to the power minus 4 upon minus 4 is equal to c1. Now multiplying both the sides by minus 4 we get y raised to the power minus 4 plus x raised to the power minus 4 is equal to minus 4 multiplied by c1. Now let us assume that this minus 4 c1 represents c. So we can write y raised to the power minus 4 plus x raised to the power minus 4 is equal to c. So the required solution of the given differential equation is x raised to the power minus 4 plus y raised to the power minus 4 is equal to c. This completes the session. Hope you understood the solution. Take care and have a nice day.