Issolvi xy^3(ydx+2xdy)+(3ydx+5xdy)=0

$$x y ^ { 3 } ( y d x + 2 x d y ) + ( 3 y d x + 5 x d y ) = 0$$

Solvi għal d

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&y=0\text{ or }x=0\text{ or }x=-\frac{8}{3y^{3}}\end{matrix}\right.$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Ikkombina ydx u 2xdy biex tikseb 3ydx.

$$xy^{3}\times 3ydx+3ydx+5xdy=0$$

Biex timmultiplika l-qawwa tal-istess bażi, żid l-esponenti tagħhom. Żid 3 u 1 biex tikseb 4.

$$xy^{4}\times 3dx+3ydx+5xdy=0$$

Immultiplika x u x biex tikseb x^{2}.

$$x^{2}y^{4}\times 3d+3ydx+5xdy=0$$

Ikkombina 3ydx u 5xdy biex tikseb 8ydx.

$$x^{2}y^{4}\times 3d+8ydx=0$$

Ikkombina t-termini kollha li fihom d.

$$\left(x^{2}y^{4}\times 3+8yx\right)d=0$$

L-ekwazzjoni hija f'forma standard.

$$\left(3x^{2}y^{4}+8xy\right)d=0$$

Iddividi 0 b'3x^{2}y^{4}+8yx.

$$d=0$$

Solvi għal x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=-\frac{8}{3y^{3}}\text{, }&y\neq 0\\x\in \mathrm{R}\text{, }&y=0\text{ or }d=0\end{matrix}\right.$$