ODE No. 390

2.390 ODE No. 390

$a y (x) y^{'} (x) - b x - c + y^{'} (x)^{2} = 0$ ✓ Mathematica : cpu = 2.39455 (sec), leaf count = 82

$Solve [{\frac{c}{b} + x = \frac{K $ 1888645 (\tan^{- 1} (\frac{\sqrt{a} K $ 1888645}{\sqrt{b - a {K $ 1888645}^{2}}}) + \sqrt{a} c_{1})}{\sqrt{a} \sqrt{b - a {K $ 1888645}^{2}}}, y (x) = \frac{b x + c - {K $ 1888645}^{2}}{a K $ 1888645}}, {y (x), K $ 1888645}]$

✓ Maple : cpu = 1.667 (sec), leaf count = 281

${y (x) = 2 \frac{(- 1 / 4 {(e^{2 R o o t O f (\sqrt{a}_C 1 b e^{2_Z} - a e^{2_Z} b x + \sqrt{a}_C 1 b^{2} - e^{2_Z}_Z b - a e^{2_Z} c + a b^{2} x -_Z b^{2} + a b c)} + b)}^{2} e^{- 2 R o o t O f (\sqrt{a}_C 1 b e^{2_Z} - a e^{2_Z} b x + \sqrt{a}_C 1 b^{2} - e^{2_Z}_Z b - a e^{2_Z} c + a b^{2} x -_Z b^{2} + a b c)} + a (b x + c)) e^{R o o t O f (\sqrt{a}_C 1 b e^{2_Z} - a e^{2_Z} b x + \sqrt{a}_C 1 b^{2} - e^{2_Z}_Z b - a e^{2_Z} c + a b^{2} x -_Z b^{2} + a b c)}}{a^{3 / 2} (e^{2 R o o t O f (\sqrt{a}_C 1 b e^{2_Z} - a e^{2_Z} b x + \sqrt{a}_C 1 b^{2} - e^{2_Z}_Z b - a e^{2_Z} c + a b^{2} x -_Z b^{2} + a b c)} + b)}}$

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