Final answer to the problem
Step-by-step Solution
Specify the solving method
Multiply the single term $x^2$ by each term of the polynomial $\left(1+y\right)$
Learn how to solve differential equations problems step by step online.
$\frac{dy}{dx}=x^2+yx^2$
Learn how to solve differential equations problems step by step online. Solve the differential equation dy/dx=x^2(1+y). Multiply the single term x^2 by each term of the polynomial \left(1+y\right). Rearrange the differential equation. 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^2 and Q(x)=x^2. 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.