 Hello, and welcome to the session. I am Deepika and I am going to help you to solve the following question the question says Solve the following differential equation x cos y dy is equal to x into e raised to power x log x plus e raised to power x dx So let's start the solution now the given differential equation is x cos y dy is equal to x into e raised to power x log x plus e raised to power x dx or this can be written as cos y dy is equal to e raised to power x into log x plus 1 over x dx now integrating both sides above equation we get integral of cos y dy is equal to integral of e raised to power x log x plus 1 over x dx Now integral of cos y dy is equal to sin y now the integral on the right hand side is of the form integral of e raised to power x into f of x plus f dash x dx and this integral is equal to e raised to power x f of x plus c So by using this integral We have sin y is equal to e raised to power x log x plus c And this is the required solution So the answer for the above question is sin y is equal to e raised to power x log x plus c So this completes our session. I hope the solution is clear to you. Bye and have a nice day