( x + y ) d y - y d x = 0
Solve for d (complex solution)
\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{C}\text{, }&y=0\end{matrix}\right.
Solve for d
\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&y=0\end{matrix}\right.
Solve for x (complex solution)
x\in \mathrm{C}
y=0\text{ or }d=0
Solve for x
x\in \mathrm{R}
y=0\text{ or }d=0
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\left(xd+yd\right)y-ydx=0
Use the distributive property to multiply x+y by d.
xdy+dy^{2}-ydx=0
Use the distributive property to multiply xd+yd by y.
dy^{2}=0
Combine xdy and -ydx to get 0.
y^{2}d=0
The equation is in standard form.
d=0
Divide 0 by y^{2}.
\left(xd+yd\right)y-ydx=0
Use the distributive property to multiply x+y by d.
xdy+dy^{2}-ydx=0
Use the distributive property to multiply xd+yd by y.
dy^{2}=0
Combine xdy and -ydx to get 0.
y^{2}d=0
The equation is in standard form.
d=0
Divide 0 by y^{2}.
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