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- 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 by parts
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We can identify that the differential equation $\left(y^2+2xy\right)dx-x^2dy=0$ 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
Learn how to solve integrals by partial fraction expansion problems step by step online.
$\left(y^2+2xy\right)dx-x^2dy=0$
Learn how to solve integrals by partial fraction expansion problems step by step online. Solve the differential equation (y^2+2xy)dx-x^2dy=0. We can identify that the differential equation \left(y^2+2xy\right)dx-x^2dy=0 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: 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.
