Final Answer
$y=\frac{e^x}{-e^x\cdot x+e^x+C_0}$
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Step-by-step Solution
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1
Rewrite the differential equation using Leibniz notation
$\frac{dy}{dx}-y=xy^2$
Learn how to solve quadratic equations problems step by step online.
$\frac{dy}{dx}-y=xy^2$
Learn how to solve quadratic equations problems step by step online. Solve the differential equation y^'-y=xy^2. Rewrite the differential equation using Leibniz notation. We identify that the differential equation \frac{dy}{dx}-y=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.
Final Answer
$y=\frac{e^x}{-e^x\cdot x+e^x+C_0}$