Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Integrate by parts
- Exact Differential Equation
- Linear Differential Equation
- Separable Differential Equation
- Homogeneous Differential Equation
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
- Integrate using tabular integration
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Rewrite the differential equation
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$\frac{dy}{dx}=\frac{y^2}{xy-x^2}$
Learn how to solve problems step by step online. Solve the differential equation (xy-x^2)dy/dx=y^2. Rewrite the differential equation. We can identify that the differential equation \frac{dy}{dx}=\frac{y^2}{xy-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: x=uy. Expand and simplify.