3.288   ODE No. 288

$$\boxed{{\displaystyle (6{\left(y\left(x\right)\right)}^2-3x^{2}y\left(x\right)+1)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-3x{\left(y\left(x\right)\right)}^2+x=0}}$$

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

Mathematica: cpu = 0.017502 (sec), leaf count = 534 $$\{\{y(x)\to -\frac{\sqrt[3]{4\sqrt{3}\sqrt{-54c_1{x}^6+648c_1{x}^2+432c_1^2-27x^8+207x^4+32}+144c_1-9x^6+108x^2}}{43^{2/3}}+\frac{6-\frac{9x^4}{4}}{3\sqrt[3]{3}\sqrt[3]{4\sqrt{3}\sqrt{-54c_1{x}^6+648c_1{x}^2+432c_1^2-27x^8+207x^4+32}+144c_1-9x^6+108x^2}}+\frac{x^2}{4}\},\{y(x)\to \frac{(1-i\sqrt{3})\sqrt[3]{4\sqrt{3}\sqrt{-54c_1{x}^6+648c_1{x}^2+432c_1^2-27x^8+207x^4+32}+144c_1-9x^6+108x^2}}{83^{2/3}}-\frac{(1+i\sqrt{3})(6-\frac{9x^4}{4})}{6\sqrt[3]{3}\sqrt[3]{4\sqrt{3}\sqrt{-54c_1{x}^6+648c_1{x}^2+432c_1^2-27x^8+207x^4+32}+144c_1-9x^6+108x^2}}+\frac{x^2}{4}\},\{y(x)\to \frac{(1+i\sqrt{3})\sqrt[3]{4\sqrt{3}\sqrt{-54c_1{x}^6+648c_1{x}^2+432c_1^2-27x^8+207x^4+32}+144c_1-9x^6+108x^2}}{83^{2/3}}-\frac{(1-i\sqrt{3})(6-\frac{9x^4}{4})}{6\sqrt[3]{3}\sqrt[3]{4\sqrt{3}\sqrt{-54c_1{x}^6+648c_1{x}^2+432c_1^2-27x^8+207x^4+32}+144c_1-9x^6+108x^2}}+\frac{x^2}{4}\}\}$$

Maple: cpu = 0.031 (sec), leaf count = 587 $$\{y\left(x\right)=\frac{1}{12}\sqrt[3]{-324x^2-432\mathit{\_}\mathit{C}\mathit{1}+27x^6+12\sqrt{-81x^8-162\mathit{\_}\mathit{C}\mathit{1}{x}^6+621x^4+1944x^2\mathit{\_}\mathit{C}\mathit{1}+1296{\mathit{\_}\mathit{C}\mathit{1}}^2+96}}-12\frac{1/6-1/16x^4}{\sqrt[3]{-324x^2-432\mathit{\_}\mathit{C}\mathit{1}+27x^6+12\sqrt{-81x^8-162\mathit{\_}\mathit{C}\mathit{1}{x}^6+621x^4+1944x^2\mathit{\_}\mathit{C}\mathit{1}+1296{\mathit{\_}\mathit{C}\mathit{1}}^2+96}}}+\frac{x^2}{4},y\left(x\right)=-\frac{1}{24}\sqrt[3]{-324x^2-432\mathit{\_}\mathit{C}\mathit{1}+27x^6+12\sqrt{-81x^8-162\mathit{\_}\mathit{C}\mathit{1}{x}^6+621x^4+1944x^2\mathit{\_}\mathit{C}\mathit{1}+1296{\mathit{\_}\mathit{C}\mathit{1}}^2+96}}+6\frac{1/6-1/16x^4}{\sqrt[3]{-324x^2-432\mathit{\_}\mathit{C}\mathit{1}+27x^6+12\sqrt{-81x^8-162\mathit{\_}\mathit{C}\mathit{1}{x}^6+621x^4+1944x^2\mathit{\_}\mathit{C}\mathit{1}+1296{\mathit{\_}\mathit{C}\mathit{1}}^2+96}}}+\frac{x^2}{4}-\frac{i}{2}\sqrt{3}(\frac{1}{12}\sqrt[3]{-324x^2-432\mathit{\_}\mathit{C}\mathit{1}+27x^6+12\sqrt{-81x^8-162\mathit{\_}\mathit{C}\mathit{1}{x}^6+621x^4+1944x^2\mathit{\_}\mathit{C}\mathit{1}+1296{\mathit{\_}\mathit{C}\mathit{1}}^2+96}}+12\frac{1/6-1/16x^4}{\sqrt[3]{-324x^2-432\mathit{\_}\mathit{C}\mathit{1}+27x^6+12\sqrt{-81x^8-162\mathit{\_}\mathit{C}\mathit{1}{x}^6+621x^4+1944x^2\mathit{\_}\mathit{C}\mathit{1}+1296{\mathit{\_}\mathit{C}\mathit{1}}^2+96}}}),y\left(x\right)=-\frac{1}{24}\sqrt[3]{-324x^2-432\mathit{\_}\mathit{C}\mathit{1}+27x^6+12\sqrt{-81x^8-162\mathit{\_}\mathit{C}\mathit{1}{x}^6+621x^4+1944x^2\mathit{\_}\mathit{C}\mathit{1}+1296{\mathit{\_}\mathit{C}\mathit{1}}^2+96}}+6\frac{1/6-1/16x^4}{\sqrt[3]{-324x^2-432\mathit{\_}\mathit{C}\mathit{1}+27x^6+12\sqrt{-81x^8-162\mathit{\_}\mathit{C}\mathit{1}{x}^6+621x^4+1944x^2\mathit{\_}\mathit{C}\mathit{1}+1296{\mathit{\_}\mathit{C}\mathit{1}}^2+96}}}+\frac{x^2}{4}+\frac{i}{2}\sqrt{3}(\frac{1}{12}\sqrt[3]{-324x^2-432\mathit{\_}\mathit{C}\mathit{1}+27x^6+12\sqrt{-81x^8-162\mathit{\_}\mathit{C}\mathit{1}{x}^6+621x^4+1944x^2\mathit{\_}\mathit{C}\mathit{1}+1296{\mathit{\_}\mathit{C}\mathit{1}}^2+96}}+12\frac{1/6-1/16x^4}{\sqrt[3]{-324x^2-432\mathit{\_}\mathit{C}\mathit{1}+27x^6+12\sqrt{-81x^8-162\mathit{\_}\mathit{C}\mathit{1}{x}^6+621x^4+1944x^2\mathit{\_}\mathit{C}\mathit{1}+1296{\mathit{\_}\mathit{C}\mathit{1}}^2+96}}})\}$$