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- Exact Differential Equation
- Linear Differential Equation
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- Homogeneous Differential Equation
- Integrate by partial fractions
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- FOIL Method
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$\frac{dy}{dx}=\frac{2x^2-2xy+y^2}{x^2}$
Learn how to solve differential equations problems step by step online. Solve the differential equation dy/dx=(2x^2-2xyy^2)/(x^2). We can identify that the differential equation \frac{dy}{dx}=\frac{2x^2-2xy+y^2}{x^2} 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.
