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- Exact Differential Equation
- Linear Differential Equation
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- Homogeneous Differential Equation
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
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Rewrite the differential equation using Leibniz notation
Learn how to solve integrals by partial fraction expansion problems step by step online.
$\frac{dy}{dx}=\frac{2x^2+2xy-y^2}{x^2}$
Learn how to solve integrals by partial fraction expansion problems step by step online. Solve the differential equation y^'=(2x^2+2xy-y^2)/(x^2). Rewrite the differential equation using Leibniz notation. 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.
