Final answer to the problem
$y+4\ln\left|y\right|=\frac{x^{3}}{3}-x+C_0$
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Step-by-step Solution
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- Exact Differential Equation
- Linear Differential Equation
- Separable Differential Equation
- Homogeneous Differential Equation
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
- Integrate by parts
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1
Factoring by $y$
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$\frac{dy}{dx}=\frac{y\left(x^2-1\right)}{y+4}$
Learn how to solve problems step by step online. Solve the differential equation dy/dx=(x^2y-y)/(y+4). Factoring by 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 \frac{1}{y}\left(y+4\right)dy. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x.
Final answer to the problem
$y+4\ln\left|y\right|=\frac{x^{3}}{3}-x+C_0$
