2.0 ODE No. 390

ODE No. 390

$a y (x) y^{'} (x) - b x - c + y^{'} (x)^{2} = 0$ ✓ Mathematica : cpu = 1.53879 (sec), leaf count = 154

DSolve[-c - b*x + a*y[x]*Derivative[1][y][x] + Derivative[1][y][x]^2 == 0,y[x],x]

$Solve [{x = (\frac{\tan^{- 1} (\frac{\sqrt{a} K [1]}{\sqrt{b - a K [1]^{2}}})}{\sqrt{a}} - \frac{c \sqrt{b - a K [1]^{2}}}{b K [1]}) \exp (b (\frac{\log (K [1])}{b} - \frac{\log (b - a K [1]^{2})}{2 b})) + c_{1} \exp (b (\frac{\log (K [1])}{b} - \frac{\log (b - a K [1]^{2})}{2 b})), y (x) = \frac{b x}{a K [1]} + \frac{c - K [1]^{2}}{a K [1]}}, {y (x), K [1]}]$ ✓ Maple : cpu = 0.592 (sec), leaf count = 281

dsolve(diff(y(x),x)^2+a*y(x)*diff(y(x),x)-b*x-c = 0,y(x))

$y (x) = \frac{2 e^{RootOf (\sqrt{a} c_{1} b e^{2_Z} - e^{2_Z} a b x + \sqrt{a} c_{1} b^{2} - e^{2_Z}_Z b - e^{2_Z} a c + a b^{2} x -_Z b^{2} + a b c)} (- \frac{{(e^{2 RootOf (\sqrt{a} c_{1} b e^{2_Z} - e^{2_Z} a b x + \sqrt{a} c_{1} b^{2} - e^{2_Z}_Z b - e^{2_Z} a c + a b^{2} x -_Z b^{2} + a b c)} + b)}^{2} e^{- 2 RootOf (\sqrt{a} c_{1} b e^{2_Z} - e^{2_Z} a b x + \sqrt{a} c_{1} b^{2} - e^{2_Z}_Z b - e^{2_Z} a c + a b^{2} x -_Z b^{2} + a b c)}}{4} + a (b x + c))}{a^{\frac{3}{2}} (e^{2 RootOf (\sqrt{a} c_{1} b e^{2_Z} - e^{2_Z} a b x + \sqrt{a} c_{1} b^{2} - e^{2_Z}_Z b - e^{2_Z} a c + a b^{2} x -_Z b^{2} + a b c)} + b)}$

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