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Multiplying polynomials $x$ and $\frac{dy}{dx}-1$
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$x\frac{dy}{dx}-x=y$
Learn how to solve problems step by step online. Solve the differential equation (dy/dx-1)x=y. Multiplying polynomials x and \frac{dy}{dx}-1. We need to isolate the dependent variable y, we can do that by simultaneously subtracting -x from both sides of the equation. Rewrite the differential equation. We can identify that the differential equation \frac{dy}{dx}=\frac{y+x}{x} 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.
