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