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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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Grouping the terms of the differential equation
Learn how to solve integration by substitution problems step by step online.
$\left(\ln\left|x\right|-\ln\left|y\right|\right)dy=\frac{-y}{x}dx$
Learn how to solve integration by substitution problems step by step online. Solve the differential equation x(ln(x)-ln(y))dy=-ydx. Grouping the terms of the differential equation. Divide both sides of the equation by dx. Rewrite the differential equation. We can identify that the differential equation \frac{dy}{dx}=\frac{-y}{x\left(\ln\left(x\right)-\ln\left(y\right)\right)} 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.
