Group the terms of the differential equation. Move the terms of the $y$ variable to the left side, and the terms of the $x$ variable to the right side of the equality
$dy=\frac{x+6}{x+1}dx$
2
Integrate both sides of the differential equation, the left side with respect to $y$, and the right side with respect to $x$
$\int1dy=\int\frac{x+6}{x+1}dx$
Intermediate steps
3
Solve the integral $\int1dy$ and replace the result in the differential equation
$y=\int\frac{x+6}{x+1}dx$
Intermediate steps
4
Solve the integral $\int\frac{x+6}{x+1}dx$ and replace the result in the differential equation
Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more