What is the solution for (ye^{xy}-1/y)dx(xe^{xy}-x/(y^2))dy=0 ?

The solution for (ye^{xy}-1/y)dx(xe^{xy}-x/(y^2))dy=0 is y=c_{1}

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(ye^{xy}-1/y)dx(xe^{xy}-x/(y^2))dy=0

(y e^{x y} - \frac{1}{y}) d x (x e^{x y} - \frac{x}{y ^{2}}) d y = 0

y = c_{1}

Solution steps

(y e^{x y} - \frac{1}{y}) d x (x e^{x y} - \frac{x}{y ^{2}}) d y = 0

Let

y

be the dependent variable. Divide by

d x

(y e^{x y} - \frac{1}{y}) (x e^{x y} - \frac{x}{y ^{2}}) \frac{d y}{d x} = 0

Substitute

\frac{d y}{d x}

with

y^{'} (x)

(y e^{x y} - \frac{1}{y}) (x e^{x y} - \frac{x}{y ^{2}}) y^{^{'}} (x) = 0

Isolate

y^{'} (x) : y^{'} (x) = 0

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

y = \int 0 d x

\int 0 d x = c_{1}

y = c_{1}

What is the solution for (ye^{xy}-1/y)dx(xe^{xy}-x/(y^2))dy=0 ?
The solution for (ye^{xy}-1/y)dx(xe^{xy}-x/(y^2))dy=0 is y=c_{1}