Final Answer
$x=-1+C_0e^{\frac{1}{2}y^2}$
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Step-by-step Solution
Problem to solve:
$\frac{dx}{dy}=y+xy$
Specify the solving method
1
Rearrange the differential equation
$\frac{dx}{dy}-xy=y$
Learn how to solve differential equations problems step by step online.
$\frac{dx}{dy}-xy=y$
Learn how to solve differential equations problems step by step online. Solve the differential equation dx/dy=y+xy. 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(y)=-y and Q(y)=y. In order to solve the differential equation, the first step is to find the integrating factor \mu(x). To find \mu(y), we first need to calculate \int P(y)dy. So the integrating factor \mu(y) is.
Final Answer
$x=-1+C_0e^{\frac{1}{2}y^2}$