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- Exact Differential Equation
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- Homogeneous Differential Equation
- Integrate by partial fractions
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We can identify that the differential equation $\frac{dy}{dx}=\frac{x^2-xy+y^2}{xy}$ is homogeneous, since it is written in the standard form $\frac{dy}{dx}=\frac{M(x,y)}{N(x,y)}$, where $M(x,y)$ and $N(x,y)$ are the partial derivatives of a two-variable function $f(x,y)$ and both are homogeneous functions of the same degree
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$\frac{dy}{dx}=\frac{x^2-xy+y^2}{xy}$
Learn how to solve problems step by step online. Solve the differential equation dy/dx=(x^2-xyy^2)/(xy). We can identify that the differential equation \frac{dy}{dx}=\frac{x^2-xy+y^2}{xy} is homogeneous, since it is written in the standard form \frac{dy}{dx}=\frac{M(x,y)}{N(x,y)}, where M(x,y) and N(x,y) are the partial derivatives of a two-variable function f(x,y) and both are homogeneous functions of the same degree. Use the substitution: y=ux. Expand and simplify. Integrate both sides of the differential equation, the left side with respect to u, and the right side with respect to x.
