d v - \sin x \sin y d x = 0
Solve for v (complex solution)
\left\{\begin{matrix}v=\frac{\sin(x)\sin(dxy)}{d}\text{, }&d\neq 0\\v\in \mathrm{C}\text{, }&\left(y=0\text{ and }n_{2}=0\text{ and }d=0\right)\text{ or }\left(\exists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}\text{ and }d=0\right)\end{matrix}\right.
Solve for v
\left\{\begin{matrix}v=\frac{\sin(x)\sin(dxy)}{d}\text{, }&d\neq 0\\v\in \mathrm{R}\text{, }&d=0\text{ and }\left(x\neq 0\text{ or }\exists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}\text{ or }y=0\right)\end{matrix}\right.
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dv=0+\sin(x)\sin(ydx)
Add \sin(x)\sin(ydx) to both sides.
dv=\sin(x)\sin(ydx)
Anything plus zero gives itself.
dv=\sin(x)\sin(dxy)
The equation is in standard form.
\frac{dv}{d}=\frac{\sin(x)\sin(dxy)}{d}
Divide both sides by d.
v=\frac{\sin(x)\sin(dxy)}{d}
Dividing by d undoes the multiplication by d.
dv=0+\sin(x)\sin(ydx)
Add \sin(x)\sin(ydx) to both sides.
dv=\sin(x)\sin(ydx)
Anything plus zero gives itself.
dv=\sin(x)\sin(dxy)
The equation is in standard form.
\frac{dv}{d}=\frac{\sin(x)\sin(dxy)}{d}
Divide both sides by d.
v=\frac{\sin(x)\sin(dxy)}{d}
Dividing by d undoes the multiplication by d.
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