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- Exact Differential Equation
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- Homogeneous Differential Equation
- Integrate by partial fractions
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- FOIL Method
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We can identify that the differential equation $y^2dx=\left(xy-x^2\right)dy$ is homogeneous, since it is written in the standard form $M(x,y)dx+N(x,y)dy=0$, 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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$y^2dx=\left(xy-x^2\right)dy$
Learn how to solve problems step by step online. Solve the differential equation y^2dx=(xy-x^2)dy. We can identify that the differential equation y^2dx=\left(xy-x^2\right)dy is homogeneous, since it is written in the standard form M(x,y)dx+N(x,y)dy=0, 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: x=uy. Expand and simplify. Group the terms of the differential equation. Move the terms of the u variable to the left side, and the terms of the y variable to the right side of the equality.
