ODE No. 970

3.970 ODE No. 970

$\frac{d}{d x} y (x) = - 216 \frac{y (x) (- 2 {(y (x))}^{4} - 3 {(y (x))}^{3} - 6 {(y (x))}^{2} - 6 y (x) + 6 x + 6)}{- 1296 x y (x) - 648 x^{2} y (x) - 1944 x {(y (x))}^{2} - 1296 y (x) + 216 x^{3} - 1296 {(y (x))}^{2} + 1728 {(y (x))}^{3} - 648 x {(y (x))}^{3} - 324 x^{2} {(y (x))}^{3} - 648 x^{2} {(y (x))}^{2} + 2808 {(y (x))}^{4} - 126 {(y (x))}^{10} - 315 {(y (x))}^{9} - 8 {(y (x))}^{12} - 36 {(y (x))}^{11} + 594 {(y (x))}^{7} + 72 {(y (x))}^{8} x + 216 {(y (x))}^{7} x + 1080 {(y (x))}^{5} x - 18 {(y (x))}^{8} + 594 x {(y (x))}^{6} - 216 x^{2} {(y (x))}^{4} + 2484 {(y (x))}^{6} - 432 x {(y (x))}^{4} + 4428 {(y (x))}^{5}} = 0$

Mathematica: cpu = 0.475060 (sec), leaf count = 66 $Solve [\frac{36 (2 y (x)^{4} + 3 y (x)^{3} + 6 y (x)^{2} + 6 y (x) - 6 x - 3)}{{(y (x) (2 y (x)^{3} + 3 y (x)^{2} + 6 y (x) + 6) - 6 x)}^{2}} + \log (y (x)) = c_{1}, y (x)]$

Maple: cpu = 0.562 (sec), leaf count = 183 ${x - \frac{1}{- 6_C 1 + 6 \ln (y (x))} (2 \ln (y (x)) {(y (x))}^{4} - 2_C 1 {(y (x))}^{4} + 3 \ln (y (x)) {(y (x))}^{3} - 3_C 1 {(y (x))}^{3} + 6 {(y (x))}^{2} \ln (y (x)) - 6_C 1 {(y (x))}^{2} + 6 y (x) \ln (y (x)) - 6 y (x)_C 1 - 6 \sqrt{3 \ln (y (x)) - 3_C 1 + 9} + 18) = 0, x - \frac{1}{- 6_C 1 + 6 \ln (y (x))} (2 \ln (y (x)) {(y (x))}^{4} - 2_C 1 {(y (x))}^{4} + 3 \ln (y (x)) {(y (x))}^{3} - 3_C 1 {(y (x))}^{3} + 6 {(y (x))}^{2} \ln (y (x)) - 6_C 1 {(y (x))}^{2} + 6 y (x) \ln (y (x)) - 6 y (x)_C 1 + 6 \sqrt{3 \ln (y (x)) - 3_C 1 + 9} + 18) = 0}$

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