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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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Rewrite the differential equation
Learn how to solve differential equations problems step by step online.
$\frac{dy}{dx}=\frac{\frac{x+y}{x}}{\frac{x-y}{x}}$
Learn how to solve differential equations problems step by step online. Solve the differential equation ((x-y)/xdy)/dx=(x+y)/x. Rewrite the differential equation. Divide fractions \frac{\frac{x+y}{x}}{\frac{x-y}{x}} with Keep, Change, Flip: \frac{a}{b}\div c=\frac{a}{b}\div\frac{c}{1}=\frac{a}{b}\times\frac{1}{c}=\frac{a}{b\cdot c}. We can identify that the differential equation \frac{dy}{dx}=\frac{x+y}{x-y} 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.
