 Hello friends welcome to the session I am Alka I am going to help you find dy by dx in the following that is 2x plus 3y equal to sin y. Now let us start with the solution our given equation is 2x plus 3y equal to sin y. Now we will differentiate both sides with respect to x this gives us 2 into dy dx of x plus 3 into dy dx of y equal to dy dx of sin y. This gives 2 into dy dx of x is 1 plus 3 into dy by dx equal to dy by dx of sin y equal to cos y into dy by dx. This can be written as 3 into dy by dx minus cos y into dy by dx equal to minus 2 or this can be written as on taking dy by dx common we get 3 minus cos y equal to minus 2. Therefore dy by dx equal to minus 2 upon 3 minus cos y now dy by dx equal to minus 2 upon on taking minus common we get cos y minus 3. We see that minus minus cancel out this gives dy by dx equal to 2 upon cos y minus 3. Therefore dy by dx equal to 2 upon cos y minus 3. Which is the required solution hope you understood it and enjoyed the session. Goodbye and take care.