Final answer to the problem
$y=\left(\sum_{n=0}^{\infty } \frac{{\left(\left(-\frac{1}{2}\right)\right)}^nx^{\left(2n+1\right)}}{\left(2n+1\right)\left(n!\right)}+C_0\right)e^{\frac{1}{2}x^2}$
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Step-by-step Solution
Learn how to solve differential equations problems step by step online. Solve the differential equation dy/dx=1+xxyy. Rearrange the differential equation. Simplifying. We can identify that the differential equation has the form: \frac{dy}{dx} + P(x)\cdot y(x) = Q(x), so we can classify it as a linear first order differential equation, where P(x)=-x and Q(x)=1. In order to solve the differential equation, the first step is to find the integrating factor \mu(x). To find \mu(x), we first need to calculate \int P(x)dx.
Final answer to the problem
$y=\left(\sum_{n=0}^{\infty } \frac{{\left(\left(-\frac{1}{2}\right)\right)}^nx^{\left(2n+1\right)}}{\left(2n+1\right)\left(n!\right)}+C_0\right)e^{\frac{1}{2}x^2}$
