x d x + y d y + ( x ^ { 2 } + y ^ { 2 } ) d y = 0
Whakaoti mō d (complex solution)
\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{C}\text{, }&y=-1\text{ or }x=iy\text{ or }x=-iy\end{matrix}\right.
Whakaoti mō d
\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&\left(y=0\text{ and }x=0\right)\text{ or }y=-1\end{matrix}\right.
Whakaoti mō x (complex solution)
\left\{\begin{matrix}\\x=-iy\text{; }x=iy\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&d=0\text{ or }y=-1\end{matrix}\right.
Whakaoti mō x
\left\{\begin{matrix}x=0\text{, }&y=0\\x\in \mathrm{R}\text{, }&d=0\text{ or }y=-1\end{matrix}\right.
Graph
Tohaina
Kua tāruatia ki te papatopenga
x^{2}d+ydy+\left(x^{2}+y^{2}\right)dy=0
Whakareatia te x ki te x, ka x^{2}.
x^{2}d+y^{2}d+\left(x^{2}+y^{2}\right)dy=0
Whakareatia te y ki te y, ka y^{2}.
x^{2}d+y^{2}d+\left(x^{2}d+y^{2}d\right)y=0
Whakamahia te āhuatanga tohatoha hei whakarea te x^{2}+y^{2} ki te d.
x^{2}d+y^{2}d+x^{2}dy+dy^{3}=0
Whakamahia te āhuatanga tohatoha hei whakarea te x^{2}d+y^{2}d ki te y.
\left(x^{2}+y^{2}+x^{2}y+y^{3}\right)d=0
Pahekotia ngā kīanga tau katoa e whai ana i te d.
\left(x^{2}+y^{3}+y^{2}+yx^{2}\right)d=0
He hanga arowhānui tō te whārite.
d=0
Whakawehe 0 ki te x^{2}+y^{2}+x^{2}y+y^{3}.
x^{2}d+ydy+\left(x^{2}+y^{2}\right)dy=0
Whakareatia te x ki te x, ka x^{2}.
x^{2}d+y^{2}d+\left(x^{2}+y^{2}\right)dy=0
Whakareatia te y ki te y, ka y^{2}.
x^{2}d+y^{2}d+\left(x^{2}d+y^{2}d\right)y=0
Whakamahia te āhuatanga tohatoha hei whakarea te x^{2}+y^{2} ki te d.
x^{2}d+y^{2}d+x^{2}dy+dy^{3}=0
Whakamahia te āhuatanga tohatoha hei whakarea te x^{2}d+y^{2}d ki te y.
\left(x^{2}+y^{2}+x^{2}y+y^{3}\right)d=0
Pahekotia ngā kīanga tau katoa e whai ana i te d.
\left(x^{2}+y^{3}+y^{2}+yx^{2}\right)d=0
He hanga arowhānui tō te whārite.
d=0
Whakawehe 0 ki te x^{2}+y^{2}+x^{2}y+y^{3}.
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