Réitigh (m^5+3y)dx-ndy=0

$$( m ^ { 5 } + 3 y ) d x - n d y = 0$$

Réitigh do d.

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&\left(n=0\text{ and }x=0\right)\text{ or }\left(y=0\text{ and }x=0\right)\text{ or }\left(m=\frac{\sqrt[5]{y\left(n-3x\right)}}{\sqrt[5]{x}}\text{ and }x\neq 0\right)\end{matrix}\right.$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Úsáid an t-airí dáileach chun m^{5}+3y a mhéadú faoi d.

$$\left(m^{5}d+3yd\right)x-ndy=0$$

Úsáid an t-airí dáileach chun m^{5}d+3yd a mhéadú faoi x.

$$m^{5}dx+3ydx-ndy=0$$

Athordaigh na téarmaí.

$$3dxy+dxm^{5}-dny=0$$

Comhcheangail na téarmaí ar fad ina bhfuil d.

$$\left(3xy+xm^{5}-ny\right)d=0$$

Roinn 0 faoi 3xy+xm^{5}-ny.

$$d=0$$

Réitigh do m.

$$\left\{\begin{matrix}m=\sqrt[5]{\frac{y\left(n-3x\right)}{x}}\text{, }&x\neq 0\\m\in \mathrm{R}\text{, }&d=0\text{ or }\left(n=0\text{ and }x=0\right)\text{ or }\left(y=0\text{ and }x=0\right)\end{matrix}\right.$$