3.247   ODE No. 247

$$\boxed{{\displaystyle (3x+2)(y\left(x\right)-2x-1)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-{\left(y\left(x\right)\right)}^2+xy\left(x\right)-7x^2-9x-3=0}}$$

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

Mathematica: cpu = 7.981514 (sec), leaf count = 693 $$\{\{y(x)\to \frac{\sqrt[3]{\sqrt{(-324e^{2c_1}x-216e^{2c_1}+1458x^3+2916x^2+1944x+432){}^2+4{(-81x^2-108x-36)}^3}-324e^{2c_1}x-216e^{2c_1}+1458x^3+2916x^2+1944x+432}}{6\sqrt[3]{2}}-\frac{-81x^2-108x-36}{32^{2/3}\sqrt[3]{\sqrt{(-324e^{2c_1}x-216e^{2c_1}+1458x^3+2916x^2+1944x+432){}^2+4{(-81x^2-108x-36)}^3}-324e^{2c_1}x-216e^{2c_1}+1458x^3+2916x^2+1944x+432}}+\frac{x}{2}\},\{y(x)\to -\frac{(1-i\sqrt{3})\sqrt[3]{\sqrt{(-324e^{2c_1}x-216e^{2c_1}+1458x^3+2916x^2+1944x+432){}^2+4{(-81x^2-108x-36)}^3}-324e^{2c_1}x-216e^{2c_1}+1458x^3+2916x^2+1944x+432}}{12\sqrt[3]{2}}+\frac{(1+i\sqrt{3})(-81x^2-108x-36)}{62^{2/3}\sqrt[3]{\sqrt{(-324e^{2c_1}x-216e^{2c_1}+1458x^3+2916x^2+1944x+432){}^2+4{(-81x^2-108x-36)}^3}-324e^{2c_1}x-216e^{2c_1}+1458x^3+2916x^2+1944x+432}}+\frac{x}{2}\},\{y(x)\to -\frac{(1+i\sqrt{3})\sqrt[3]{\sqrt{(-324e^{2c_1}x-216e^{2c_1}+1458x^3+2916x^2+1944x+432){}^2+4{(-81x^2-108x-36)}^3}-324e^{2c_1}x-216e^{2c_1}+1458x^3+2916x^2+1944x+432}}{12\sqrt[3]{2}}+\frac{(1-i\sqrt{3})(-81x^2-108x-36)}{62^{2/3}\sqrt[3]{\sqrt{(-324e^{2c_1}x-216e^{2c_1}+1458x^3+2916x^2+1944x+432){}^2+4{(-81x^2-108x-36)}^3}-324e^{2c_1}x-216e^{2c_1}+1458x^3+2916x^2+1944x+432}}+\frac{x}{2}\}\}$$

Maple: cpu = 0.156 (sec), leaf count = 517 $$\{y\left(x\right)=-\frac{1}{3}+\frac{3x+2}{6}(7{(-1/4\sqrt[3]{2(3x+2)\mathit{\_}\mathit{C}\mathit{1}-27{(3x+2)}^3{\mathit{\_}\mathit{C}\mathit{1}}^3+2\sqrt{-27{(3x+2)}^4{\mathit{\_}\mathit{C}\mathit{1}}^4+{(3x+2)}^2{\mathit{\_}\mathit{C}\mathit{1}}^2}}-9/4\frac{{(3x+2)}^2{\mathit{\_}\mathit{C}\mathit{1}}^2}{\sqrt[3]{2(3x+2)\mathit{\_}\mathit{C}\mathit{1}-27{(3x+2)}^3{\mathit{\_}\mathit{C}\mathit{1}}^3+2\sqrt{-27{(3x+2)}^4{\mathit{\_}\mathit{C}\mathit{1}}^4+{(3x+2)}^2{\mathit{\_}\mathit{C}\mathit{1}}^2}}}-3/2(3x+2)\mathit{\_}\mathit{C}\mathit{1}+i/2\sqrt{3}(1/2\sqrt[3]{2(3x+2)\mathit{\_}\mathit{C}\mathit{1}-27{(3x+2)}^3{\mathit{\_}\mathit{C}\mathit{1}}^3+2\sqrt{-27{(3x+2)}^4{\mathit{\_}\mathit{C}\mathit{1}}^4+{(3x+2)}^2{\mathit{\_}\mathit{C}\mathit{1}}^2}}-9/2\frac{{(3x+2)}^2{\mathit{\_}\mathit{C}\mathit{1}}^2}{\sqrt[3]{2(3x+2)\mathit{\_}\mathit{C}\mathit{1}-27{(3x+2)}^3{\mathit{\_}\mathit{C}\mathit{1}}^3+2\sqrt{-27{(3x+2)}^4{\mathit{\_}\mathit{C}\mathit{1}}^4+{(3x+2)}^2{\mathit{\_}\mathit{C}\mathit{1}}^2}}}))}^2-1){(-\frac{1}{4}\sqrt[3]{2(3x+2)\mathit{\_}\mathit{C}\mathit{1}-27{(3x+2)}^3{\mathit{\_}\mathit{C}\mathit{1}}^3+2\sqrt{-27{(3x+2)}^4{\mathit{\_}\mathit{C}\mathit{1}}^4+{(3x+2)}^2{\mathit{\_}\mathit{C}\mathit{1}}^2}}-\frac{9{(3x+2)}^2{\mathit{\_}\mathit{C}\mathit{1}}^2}{4}\frac{1}{\sqrt[3]{2(3x+2)\mathit{\_}\mathit{C}\mathit{1}-27{(3x+2)}^3{\mathit{\_}\mathit{C}\mathit{1}}^3+2\sqrt{-27{(3x+2)}^4{\mathit{\_}\mathit{C}\mathit{1}}^4+{(3x+2)}^2{\mathit{\_}\mathit{C}\mathit{1}}^2}}}-\frac{(9x+6)\mathit{\_}\mathit{C}\mathit{1}}{2}+\frac{i}{2}\sqrt{3}(\frac{1}{2}\sqrt[3]{2(3x+2)\mathit{\_}\mathit{C}\mathit{1}-27{(3x+2)}^3{\mathit{\_}\mathit{C}\mathit{1}}^3+2\sqrt{-27{(3x+2)}^4{\mathit{\_}\mathit{C}\mathit{1}}^4+{(3x+2)}^2{\mathit{\_}\mathit{C}\mathit{1}}^2}}-\frac{9{(3x+2)}^2{\mathit{\_}\mathit{C}\mathit{1}}^2}{2}\frac{1}{\sqrt[3]{2(3x+2)\mathit{\_}\mathit{C}\mathit{1}-27{(3x+2)}^3{\mathit{\_}\mathit{C}\mathit{1}}^3+2\sqrt{-27{(3x+2)}^4{\mathit{\_}\mathit{C}\mathit{1}}^4+{(3x+2)}^2{\mathit{\_}\mathit{C}\mathit{1}}^2}}}))}^{-2}\}$$