( x + y ^ { 2 } ) d y = y d x
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+y^{2}d\right)y=ydx
Use the distributive property to multiply x+y^{2} by d.
xdy+dy^{3}=ydx
Use the distributive property to multiply xd+y^{2}d by y.
xdy+dy^{3}-ydx=0
Subtract ydx from both sides.
dy^{3}=0
Combine xdy and -ydx to get 0.
y^{3}d=0
The equation is in standard form.
d=0
Divide 0 by y^{3}.
\left(xd+y^{2}d\right)y=ydx
Use the distributive property to multiply x+y^{2} by d.
xdy+dy^{3}=ydx
Use the distributive property to multiply xd+y^{2}d by y.
xdy+dy^{3}-ydx=0
Subtract ydx from both sides.
dy^{3}=0
Combine xdy and -ydx to get 0.
y^{3}d=0
The equation is in standard form.
d=0
Divide 0 by y^{3}.
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