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We identify that the differential equation $\frac{dy}{dx}+\frac{y}{x}=-xy^2$ 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
Learn how to solve integrals of polynomial functions problems step by step online.
$u=y^{\left(1-n\right)}$
Learn how to solve integrals of polynomial functions problems step by step online. Solve the differential equation dy/dx+y/x=-xy^2. We identify that the differential equation \frac{dy}{dx}+\frac{y}{x}=-xy^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. Simplify. Isolate the dependent variable y.
