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Calculus 2: Introduction to differential equations

Name the order, linearity (linear or non-linear), and homogeneity (homogeneous or non-homogeneous) of the following differential equations.

Find the particular solution of the differential equation with initial condition y(e)=ey(e) = e.

Solve the differential equation: dydx=x+xy2\frac{dy}{dx} = x + x y^2 with the initial condition y(0)=1y(0) = -1.