ODE No. 64

2.64 ODE No. 64

Problem in Latex
Mathematica input
Maple input

$y^{'} (x) - \sqrt{\frac{a y (x)^{2} + b y (x) + c}{a x^{2} + b x + c}} = 0$ ✓ Mathematica : cpu = 0.193224 (sec), leaf count = 90

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

✓ Maple : cpu = 0.109 (sec), leaf count = 124

${- 1 \sqrt{\frac{a {(y (x))}^{2} + b y (x) + c}{a x^{2} + b x + c}} \sqrt{a x^{2} + b x + c} \ln (\frac{1}{2} (2 \sqrt{a x^{2} + b x + c} \sqrt{a} + 2 a x + b) \frac{1}{\sqrt{a}}) \frac{1}{\sqrt{a {(y (x))}^{2} + b y (x) + c}} \frac{1}{\sqrt{a}} + 1 \ln (\sqrt{a {(y (x))}^{2} + b y (x) + c} + \frac{2 a y (x) + b}{2} \frac{1}{\sqrt{a}}) \frac{1}{\sqrt{a}} +_C 1 = 0}$

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