ODE No. 1795

8.205 ODE No. 1795

$x {(y (x))}^{2} \frac{d^{2}}{d x^{2}} y (x) - a = 0$

Mathematica: cpu = 0.259533 (sec), leaf count = 116 $Solve [- \frac{\sqrt{- \frac{2 a y (x)}{x} - \frac{2 c_{1} y (x)^{2}}{x^{2}}}}{2 c_{1}} - \frac{a \tan^{- 1} (\frac{\sqrt{2} \sqrt{c_{1}} (\frac{a}{2 c_{1}} + \frac{y (x)}{x})}{\sqrt{- \frac{2 a y (x)}{x} - \frac{2 c_{1} y (x)^{2}}{x^{2}}}})}{2 \sqrt{2} c_{1}^{3 / 2}} - c_{2} - \frac{1}{x} = 0, y (x)]$

Maple: cpu = 2.262 (sec), leaf count = 793 ${y (x) = \frac{_C 1 x (81 {_C 1}^{2} a^{2} + 18 a_C 1 e^{R o o t O f (243 c s g n ({_C 1}^{- 1}) {_C 1}^{4} a^{2} x - 54_Z e^{_Z} a x {_C 1}^{3} - 3 c s g n ({_C 1}^{- 1}) {(e^{_Z})}^{2} {_C 1}^{2} x - 6 c s g n ({_C 1}^{- 1}) e^{_Z}_C 2 x - 2 c s g n ({_C 1}^{- 1}) e^{_Z})} + {(e^{R o o t O f (243 c s g n ({_C 1}^{- 1}) {_C 1}^{4} a^{2} x - 54_Z e^{_Z} a x {_C 1}^{3} - 3 c s g n ({_C 1}^{- 1}) {(e^{_Z})}^{2} {_C 1}^{2} x - 6 c s g n ({_C 1}^{- 1}) e^{_Z}_C 2 x - 2 c s g n ({_C 1}^{- 1}) e^{_Z})})}^{2})}{2 e^{R o o t O f (243 c s g n ({_C 1}^{- 1}) {_C 1}^{4} a^{2} x - 54_Z e^{_Z} a x {_C 1}^{3} - 3 c s g n ({_C 1}^{- 1}) {(e^{_Z})}^{2} {_C 1}^{2} x - 6 c s g n ({_C 1}^{- 1}) e^{_Z}_C 2 x - 2 c s g n ({_C 1}^{- 1}) e^{_Z})}}, y (x) = \frac{_C 1 x (81 {_C 1}^{2} a^{2} + 18 a_C 1 e^{R o o t O f (243 c s g n ({_C 1}^{- 1}) {_C 1}^{4} a^{2} x - 54_Z e^{_Z} a x {_C 1}^{3} - 3 c s g n ({_C 1}^{- 1}) {(e^{_Z})}^{2} {_C 1}^{2} x + 6 c s g n ({_C 1}^{- 1}) e^{_Z}_C 2 x + 2 c s g n ({_C 1}^{- 1}) e^{_Z})} + {(e^{R o o t O f (243 c s g n ({_C 1}^{- 1}) {_C 1}^{4} a^{2} x - 54_Z e^{_Z} a x {_C 1}^{3} - 3 c s g n ({_C 1}^{- 1}) {(e^{_Z})}^{2} {_C 1}^{2} x + 6 c s g n ({_C 1}^{- 1}) e^{_Z}_C 2 x + 2 c s g n ({_C 1}^{- 1}) e^{_Z})})}^{2})}{2 e^{R o o t O f (243 c s g n ({_C 1}^{- 1}) {_C 1}^{4} a^{2} x - 54_Z e^{_Z} a x {_C 1}^{3} - 3 c s g n ({_C 1}^{- 1}) {(e^{_Z})}^{2} {_C 1}^{2} x + 6 c s g n ({_C 1}^{- 1}) e^{_Z}_C 2 x + 2 c s g n ({_C 1}^{- 1}) e^{_Z})}}, y (x) = \frac{_C 1 x (81 {_C 1}^{2} a^{2} + 18 a_C 1 e^{R o o t O f (243 c s g n ({_C 1}^{- 1}) {_C 1}^{4} a^{2} x + 54_Z e^{_Z} a x {_C 1}^{3} - 3 c s g n ({_C 1}^{- 1}) {(e^{_Z})}^{2} {_C 1}^{2} x - 6 c s g n ({_C 1}^{- 1}) e^{_Z}_C 2 x - 2 c s g n ({_C 1}^{- 1}) e^{_Z})} + {(e^{R o o t O f (243 c s g n ({_C 1}^{- 1}) {_C 1}^{4} a^{2} x + 54_Z e^{_Z} a x {_C 1}^{3} - 3 c s g n ({_C 1}^{- 1}) {(e^{_Z})}^{2} {_C 1}^{2} x - 6 c s g n ({_C 1}^{- 1}) e^{_Z}_C 2 x - 2 c s g n ({_C 1}^{- 1}) e^{_Z})})}^{2})}{2 e^{R o o t O f (243 c s g n ({_C 1}^{- 1}) {_C 1}^{4} a^{2} x + 54_Z e^{_Z} a x {_C 1}^{3} - 3 c s g n ({_C 1}^{- 1}) {(e^{_Z})}^{2} {_C 1}^{2} x - 6 c s g n ({_C 1}^{- 1}) e^{_Z}_C 2 x - 2 c s g n ({_C 1}^{- 1}) e^{_Z})}}, y (x) = \frac{_C 1 x (81 {_C 1}^{2} a^{2} + 18 a_C 1 e^{R o o t O f (243 c s g n ({_C 1}^{- 1}) {_C 1}^{4} a^{2} x + 54_Z e^{_Z} a x {_C 1}^{3} - 3 c s g n ({_C 1}^{- 1}) {(e^{_Z})}^{2} {_C 1}^{2} x + 6 c s g n ({_C 1}^{- 1}) e^{_Z}_C 2 x + 2 c s g n ({_C 1}^{- 1}) e^{_Z})} + {(e^{R o o t O f (243 c s g n ({_C 1}^{- 1}) {_C 1}^{4} a^{2} x + 54_Z e^{_Z} a x {_C 1}^{3} - 3 c s g n ({_C 1}^{- 1}) {(e^{_Z})}^{2} {_C 1}^{2} x + 6 c s g n ({_C 1}^{- 1}) e^{_Z}_C 2 x + 2 c s g n ({_C 1}^{- 1}) e^{_Z})})}^{2})}{2 e^{R o o t O f (243 c s g n ({_C 1}^{- 1}) {_C 1}^{4} a^{2} x + 54_Z e^{_Z} a x {_C 1}^{3} - 3 c s g n ({_C 1}^{- 1}) {(e^{_Z})}^{2} {_C 1}^{2} x + 6 c s g n ({_C 1}^{- 1}) e^{_Z}_C 2 x + 2 c s g n ({_C 1}^{- 1}) e^{_Z})}}}$

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