Final answer to the problem
$y+7-7\ln\left|y+7\right|-2\ln\left|y+7\right|=x+8-8\ln\left|x+8\right|-\ln\left|x+8\right|+C_0$
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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 $x-1$
Learn how to solve integration techniques problems step by step online.
$\frac{dy}{dx}=\frac{\left(x-1\right)\left(y+7\right)}{x\left(y-2\right)+8\left(y-2\right)}$
Learn how to solve integration techniques problems step by step online. Solve the differential equation dy/dx=(y(x-1)+7(x-1))/(x(y-2)+8(y-2)). Factoring by x-1. Factoring by 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+7}\left(y-2\right)dy.
Final answer to the problem
$y+7-7\ln\left|y+7\right|-2\ln\left|y+7\right|=x+8-8\ln\left|x+8\right|-\ln\left|x+8\right|+C_0$
