( 2 y - 3 x ) d x + x d y = 0
Solve for d (complex solution)
\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{C}\text{, }&y=x\text{ or }x=0\end{matrix}\right.
Solve for d
\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&y=x\text{ or }x=0\end{matrix}\right.
Solve for x (complex solution)
\left\{\begin{matrix}\\x=y\text{; }x=0\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&d=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}\\x=y\text{; }x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&d=0\end{matrix}\right.
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\left(2yd-3xd\right)x+xdy=0
Use the distributive property to multiply 2y-3x by d.
2ydx-3dx^{2}+xdy=0
Use the distributive property to multiply 2yd-3xd by x.
3ydx-3dx^{2}=0
Combine 2ydx and xdy to get 3ydx.
\left(3yx-3x^{2}\right)d=0
Combine all terms containing d.
\left(3xy-3x^{2}\right)d=0
The equation is in standard form.
d=0
Divide 0 by 3yx-3x^{2}.
\left(2yd-3xd\right)x+xdy=0
Use the distributive property to multiply 2y-3x by d.
2ydx-3dx^{2}+xdy=0
Use the distributive property to multiply 2yd-3xd by x.
3ydx-3dx^{2}=0
Combine 2ydx and xdy to get 3ydx.
\left(3yx-3x^{2}\right)d=0
Combine all terms containing d.
\left(3xy-3x^{2}\right)d=0
The equation is in standard form.
d=0
Divide 0 by 3yx-3x^{2}.
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