Final answer to the problem
$y=\frac{1}{x\left(8\ln\left(x\right)+C_0\right)}$
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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
Rewrite the differential equation in standard form
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$\frac{dy}{dx}+\frac{y}{x}=\frac{-8xy^2}{x}$
Learn how to solve problems step by step online. Solve the differential equation xdy/dx+y=-8xy^2. Rewrite the differential equation in standard form. Simplify the fraction \frac{-8xy^2}{x} by x. We identify that the differential equation \frac{dy}{dx}+\frac{y}{x}=-8y^2 is a Bernoulli differential equation since it's of the form \frac{dy}{dx}+P(x)y=Q(x)y^n, where n is any real number different from 0 and 1. To solve this equation, we can apply the following substitution. Let's define a new variable u and set it equal to. Plug in the value of n, which equals 2.
Final answer to the problem
$y=\frac{1}{x\left(8\ln\left(x\right)+C_0\right)}$
