\frac { d y } { d x } + 5 x d y = 0
Solve for d
\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&y=0\text{ or }x=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&y=0\text{ or }d=0\end{matrix}\right.
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5xdy=-\frac{\mathrm{d}(y)}{\mathrm{d}x}
Subtract \frac{\mathrm{d}(y)}{\mathrm{d}x} from both sides. Anything subtracted from zero gives its negation.
5xyd=0
The equation is in standard form.
d=0
Divide 0 by 5xy.
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