Issolvi dx/dt=kx^n(1-x)^n

$$\frac { d x } { d t } = k x ^ { n } ( 1 - x ) ^ { n }$$

Solvi għal k

$$\left\{\begin{matrix}k=0\text{, }&\left(x>0\text{ and }x<1\right)\text{ or }\left(n>0\text{ and }x=1\right)\text{ or }\left(Denominator(n)\text{bmod}2=1\text{ and }x>1\right)\text{ or }\left(n>0\text{ and }x=0\right)\text{ or }\left(Denominator(n)\text{bmod}2=1\text{ and }x<0\right)\\k\in \mathrm{R}\text{, }&\left(x=1\text{ or }x=0\right)\text{ and }n>0\end{matrix}\right.$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Ibdel in-naħat sabiex it-termini varjabbli kollha jkunu fuq in-naħa tax-xellug.

$$kx^{n}\left(1-x\right)^{n}=\frac{\mathrm{d}}{\mathrm{d}t}(x)$$

L-ekwazzjoni hija f'forma standard.

$$\left(x\left(1-x\right)\right)^{n}k=0$$

Iddividi 0 b'x^{n}\left(1-x\right)^{n}.

$$k=0$$

Solvi għal n

$$\left\{\begin{matrix}n\in \mathrm{R}\text{, }&\left(x>0\text{ or }Denominator(n)\text{bmod}2=1\right)\text{ and }x\neq 1\text{ and }x\neq 0\text{ and }k=0\text{ and }\left(x<1\text{ or }Denominator(n)\text{bmod}2=1\right)\\n>0\text{, }&x=1\text{ or }x=0\end{matrix}\right.$$