Exercise
$\frac{dy}{dx}=\frac{y\left(x-1\right)^2}{y+3}$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation dy/dx=(y(x-1)^2)/(y+3). 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 \frac{1}{y}\left(y+3\right)dy. Simplify the expression \left(x-1\right)^2dx. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x.
Solve the differential equation dy/dx=(y(x-1)^2)/(y+3)
Final answer to the exercise
$y+3\ln\left|y\right|=\frac{x^{3}}{3}-x^2+x+C_0$