3.382   ODE No. 382

$$\boxed{{\displaystyle {\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2+ax\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-b{x}^2-c=0}}$$

1. Problem in Latex
2. Mathematica input
3. Maple input

Mathematica: cpu = 0.255032 (sec), leaf count = 201 $$\{\{y(x)\to \frac{1}{2}(\frac{1}{2}x\sqrt{a^2{x}^2+4b{x}^2+4c}+\frac{2c\log (\sqrt{a^2+4b}\sqrt{a^2{x}^2+4b{x}^2+4c}+a^{2}x+4bx)}{\sqrt{a^2+4b}}-\frac{a{x}^2}{2})+c_1\},\{y(x)\to \frac{1}{2}(-\frac{1}{2}x(\sqrt{x^2(a^2+4b)+4c}+ax)-\frac{2c\log (\sqrt{a^2+4b}\sqrt{x^2(a^2+4b)+4c}+a^{2}x+4bx)}{\sqrt{a^2+4b}})+c_1\}\}$$

Maple: cpu = 0.390 (sec), leaf count = 146 $$\{y\left(x\right)=-\frac{a{x}^2}{4}-\frac{x}{4}\sqrt{(a^2+4b)x^2+4c}-c\ln (\sqrt{a^2+4b}x+\sqrt{(a^2+4b)x^2+4c})\frac{1}{\sqrt{a^2+4b}}+\mathit{\_}\mathit{C}\mathit{1},y\left(x\right)=-\frac{a{x}^2}{4}+\frac{x}{4}\sqrt{(a^2+4b)x^2+4c}+c\ln (\sqrt{a^2+4b}x+\sqrt{(a^2+4b)x^2+4c})\frac{1}{\sqrt{a^2+4b}}+\mathit{\_}\mathit{C}\mathit{1}\}$$