Issolvi (x^2-y^2)dx+(x^2+y^2)dy=0

$$( x ^ { 2 } - y ^ { 2 } ) d x + ( x ^ { 2 } + y ^ { 2 } ) d y = 0$$

Solvi għal d

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&x=\frac{\sqrt[3]{3\sqrt{33}\left(|y|\right)^{3}-19y^{3}}+\sqrt[3]{-3\sqrt{33}\left(|y|\right)^{3}-19y^{3}}-y}{3}\end{matrix}\right.$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Uża l-propjetà distributtiva biex timmultiplika x^{2}-y^{2} b'd.

$$\left(x^{2}d-y^{2}d\right)x+\left(x^{2}+y^{2}\right)dy=0$$

Uża l-propjetà distributtiva biex timmultiplika x^{2}d-y^{2}d b'x.

$$dx^{3}-y^{2}dx+\left(x^{2}+y^{2}\right)dy=0$$

Uża l-propjetà distributtiva biex timmultiplika x^{2}+y^{2} b'd.

$$dx^{3}-y^{2}dx+\left(x^{2}d+y^{2}d\right)y=0$$

Uża l-propjetà distributtiva biex timmultiplika x^{2}d+y^{2}d b'y.

$$dx^{3}-y^{2}dx+x^{2}dy+dy^{3}=0$$

Ikkombina t-termini kollha li fihom d.

$$\left(x^{3}-y^{2}x+x^{2}y+y^{3}\right)d=0$$

L-ekwazzjoni hija f'forma standard.

$$\left(x^{3}-xy^{2}+y^{3}+yx^{2}\right)d=0$$

Iddividi 0 b'x^{3}-y^{2}x+x^{2}y+y^{3}.

$$d=0$$

Solvi għal x

$$\left\{\begin{matrix}\\x=\frac{\sqrt[3]{3\sqrt{33}\left(|y|\right)^{3}-19y^{3}}+\sqrt[3]{-3\sqrt{33}\left(|y|\right)^{3}-19y^{3}}-y}{3}\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&d=0\end{matrix}\right.$$