Exercise
$\frac{dy}{dx}=\frac{x+1}{3y^2+y}$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation dy/dx=(x+1)/(3y^2+y). 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. Simplify the expression \left(3y^2+y\right)dy. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x. Expand the integral \int\left(x+1\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately.
Solve the differential equation dy/dx=(x+1)/(3y^2+y)
Final answer to the exercise
$y^{3}+\frac{1}{2}y^2=\frac{1}{2}x^2+x+C_0$