Final answer to the problem
$\frac{1}{2}\ln\left|y\right|-\frac{1}{2}\ln\left|y+2\right|=x+C_0$
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Step-by-step Solution
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- Equation différentielle exacte
- Équation différentielle linéaire
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- Produit de binômes avec terme commun
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1
Apply the formula: $\frac{dy}{dx}+a=b$$\to \frac{dy}{dx}=b-a$, where $a=-2y$ and $b=y^2$
$\frac{dy}{dx}=y^2+2y$
Learn how to solve equations logarithmiques problems step by step online.
$\frac{dy}{dx}=y^2+2y$
Learn how to solve equations logarithmiques problems step by step online. dy/dx-2y=y^2. Apply the formula: \frac{dy}{dx}+a=b\to \frac{dy}{dx}=b-a, where a=-2y and b=y^2. 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^2+2y}dy. Apply the formula: b\cdot dy=dx\to \int bdy=\int1dx, where b=\frac{1}{y\left(y+2\right)}.
Final answer to the problem
$\frac{1}{2}\ln\left|y\right|-\frac{1}{2}\ln\left|y+2\right|=x+C_0$
