ODE No. 54

3.54 ODE No. 54

$\frac{d}{d x} y (x) - a^{n} {(f (x))}^{1 - n} (\frac{d}{d x} g (x)) {(y (x))}^{n} - \frac{(\frac{d}{d x} f (x)) y (x)}{f (x)} - f (x) \frac{d}{d x} g (x) = 0$

Mathematica: cpu = 0.116515 (sec), leaf count = 74 $Solve [y (x) {(a^{n} f (x)^{- n})}^{\frac{1}{n}}_{2} F_{1} (1, \frac{1}{n}; 1 + \frac{1}{n}; - {({(a^{n} f (x)^{- n})}^{\frac{1}{n}} y (x))}^{n}) = f (x) g (x) {(a^{n} f (x)^{- n})}^{\frac{1}{n}} + c_{1}, y (x)]$

Maple: cpu = 0.124 (sec), leaf count = 42 ${_C 1 + \frac{y (x)}{f (x)}_{2} F_{1} (1, n^{- 1}; \frac{n + 1}{n}; - {(\frac{a y (x)}{f (x)})}^{n}) - g (x) = 0}$

Sage: cpu = 1.384 (sec), leaf count = 0 $[[\int \frac{a^{n} y {(x)}^{n} f {(x)}^{2} D [0] (g) (x) + f {(x)}^{n} y (x) D [0] (f) (x) + f {(x)}^{n + 2} D [0] (g) (x)}{a^{n} y {(x)}^{n} f {(x)}^{2} + f {(x)}^{n + 2}} d x + \int \frac{(a^{n} y {(x)}^{n} f (x) + f {(x)}^{n + 1}) \int \frac{(a^{n} n - a^{n}) f {(x)}^{n} y {(x)}^{n} D [0] (f) (x) - f {(x)}^{2 n} D [0] (f) (x)}{a^{2 n} y {(x)}^{2 n} f {(x)}^{2} + 2 a^{n} f {(x)}^{n + 2} y {(x)}^{n} + f {(x)}^{2 n + 2}} d x - f {(x)}^{n}}{a^{n} y {(x)}^{n} f (x) + f {(x)}^{n + 1}} d (y (x)) = c], lie]$

[next] [prev] [prev-tail] [front] [up]