3.738   ODE No. 738

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=2\frac{a}{-x^{2}y\left(x\right)+2a{\left(y\left(x\right)\right)}^4{x}^2-16a^{2}x{\left(y\left(x\right)\right)}^2+32a^3}=0}}$$

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

Mathematica: cpu = 0.515566 (sec), leaf count = 1347 $$\{\{y(x)\to -\frac{4a+e^{c_1}}{12a}+\frac{\sqrt[3]{4608x^2{a}^4-128x^3{a}^3+1152e^{c_1}{x}^2{a}^3-96e^{c_1}{x}^3{a}^2-432x^3{a}^2-24e^{2c_1}{x}^{3}a-2e^{3c_1}{x}^3+\sqrt{4(-192x{a}^3-(4a+e^{c_1}){}^2{x}^2){}^3+(4608x^2{a}^4-128x^3{a}^3+1152e^{c_1}{x}^2{a}^3-96e^{c_1}{x}^3{a}^2-432x^3{a}^2-24e^{2c_1}{x}^{3}a-2e^{3c_1}{x}^3){}^2}}}{12\sqrt[3]{2}ax}-\frac{-192x{a}^3-(4a+e^{c_1}){}^2{x}^2}{62^{2/3}ax\sqrt[3]{4608x^2{a}^4-128x^3{a}^3+1152e^{c_1}{x}^2{a}^3-96e^{c_1}{x}^3{a}^2-432x^3{a}^2-24e^{2c_1}{x}^{3}a-2e^{3c_1}{x}^3+\sqrt{4(-192x{a}^3-(4a+e^{c_1}){}^2{x}^2){}^3+(4608x^2{a}^4-128x^3{a}^3+1152e^{c_1}{x}^2{a}^3-96e^{c_1}{x}^3{a}^2-432x^3{a}^2-24e^{2c_1}{x}^{3}a-2e^{3c_1}{x}^3){}^2}}}\},\{y(x)\to -\frac{4a+e^{c_1}}{12a}-\frac{(1-i\sqrt{3})\sqrt[3]{4608x^2{a}^4-128x^3{a}^3+1152e^{c_1}{x}^2{a}^3-96e^{c_1}{x}^3{a}^2-432x^3{a}^2-24e^{2c_1}{x}^{3}a-2e^{3c_1}{x}^3+\sqrt{4(-192x{a}^3-(4a+e^{c_1}){}^2{x}^2){}^3+(4608x^2{a}^4-128x^3{a}^3+1152e^{c_1}{x}^2{a}^3-96e^{c_1}{x}^3{a}^2-432x^3{a}^2-24e^{2c_1}{x}^{3}a-2e^{3c_1}{x}^3){}^2}}}{24\sqrt[3]{2}ax}+\frac{(1+i\sqrt{3})(-192x{a}^3-(4a+e^{c_1}){}^2{x}^2)}{122^{2/3}ax\sqrt[3]{4608x^2{a}^4-128x^3{a}^3+1152e^{c_1}{x}^2{a}^3-96e^{c_1}{x}^3{a}^2-432x^3{a}^2-24e^{2c_1}{x}^{3}a-2e^{3c_1}{x}^3+\sqrt{4(-192x{a}^3-(4a+e^{c_1}){}^2{x}^2){}^3+(4608x^2{a}^4-128x^3{a}^3+1152e^{c_1}{x}^2{a}^3-96e^{c_1}{x}^3{a}^2-432x^3{a}^2-24e^{2c_1}{x}^{3}a-2e^{3c_1}{x}^3){}^2}}}\},\{y(x)\to -\frac{4a+e^{c_1}}{12a}-\frac{(1+i\sqrt{3})\sqrt[3]{4608x^2{a}^4-128x^3{a}^3+1152e^{c_1}{x}^2{a}^3-96e^{c_1}{x}^3{a}^2-432x^3{a}^2-24e^{2c_1}{x}^{3}a-2e^{3c_1}{x}^3+\sqrt{4(-192x{a}^3-(4a+e^{c_1}){}^2{x}^2){}^3+(4608x^2{a}^4-128x^3{a}^3+1152e^{c_1}{x}^2{a}^3-96e^{c_1}{x}^3{a}^2-432x^3{a}^2-24e^{2c_1}{x}^{3}a-2e^{3c_1}{x}^3){}^2}}}{24\sqrt[3]{2}ax}+\frac{(1-i\sqrt{3})(-192x{a}^3-(4a+e^{c_1}){}^2{x}^2)}{122^{2/3}ax\sqrt[3]{4608x^2{a}^4-128x^3{a}^3+1152e^{c_1}{x}^2{a}^3-96e^{c_1}{x}^3{a}^2-432x^3{a}^2-24e^{2c_1}{x}^{3}a-2e^{3c_1}{x}^3+\sqrt{4(-192x{a}^3-(4a+e^{c_1}){}^2{x}^2){}^3+(4608x^2{a}^4-128x^3{a}^3+1152e^{c_1}{x}^2{a}^3-96e^{c_1}{x}^3{a}^2-432x^3{a}^2-24e^{2c_1}{x}^{3}a-2e^{3c_1}{x}^3){}^2}}}\}\}$$

Maple: cpu = 0.561 (sec), leaf count = 1096 $$\{y\left(x\right)=\frac{1}{12\mathit{\_}\mathit{C}\mathit{1}ax}\sqrt[3]{(-216{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^{2}x+576a^3{\mathit{\_}\mathit{C}\mathit{1}}^2+12\sqrt{-\frac{49152{\mathit{\_}\mathit{C}\mathit{1}}^4{a}^7-324{\mathit{\_}\mathit{C}\mathit{1}}^4{a}^2{x}^3+1728{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^3{x}^2-1536{\mathit{\_}\mathit{C}\mathit{1}}^2{a}^{4}x-3\mathit{\_}\mathit{C}\mathit{1}{x}^3+12a{x}^2}{x}}\mathit{\_}\mathit{C}\mathit{1}a-x)x^2}+\frac{192a^3{\mathit{\_}\mathit{C}\mathit{1}}^2+x}{12\mathit{\_}\mathit{C}\mathit{1}a}\frac{1}{\sqrt[3]{(-216{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^{2}x+576a^3{\mathit{\_}\mathit{C}\mathit{1}}^2+12\sqrt{-\frac{49152{\mathit{\_}\mathit{C}\mathit{1}}^4{a}^7-324{\mathit{\_}\mathit{C}\mathit{1}}^4{a}^2{x}^3+1728{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^3{x}^2-1536{\mathit{\_}\mathit{C}\mathit{1}}^2{a}^{4}x-3\mathit{\_}\mathit{C}\mathit{1}{x}^3+12a{x}^2}{x}}\mathit{\_}\mathit{C}\mathit{1}a-x)x^2}}-\frac{1}{12\mathit{\_}\mathit{C}\mathit{1}a},y\left(x\right)=-\frac{1}{24\mathit{\_}\mathit{C}\mathit{1}ax}\sqrt[3]{(-216{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^{2}x+576a^3{\mathit{\_}\mathit{C}\mathit{1}}^2+12\sqrt{-\frac{49152{\mathit{\_}\mathit{C}\mathit{1}}^4{a}^7-324{\mathit{\_}\mathit{C}\mathit{1}}^4{a}^2{x}^3+1728{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^3{x}^2-1536{\mathit{\_}\mathit{C}\mathit{1}}^2{a}^{4}x-3\mathit{\_}\mathit{C}\mathit{1}{x}^3+12a{x}^2}{x}}\mathit{\_}\mathit{C}\mathit{1}a-x)x^2}-\frac{192a^3{\mathit{\_}\mathit{C}\mathit{1}}^2+x}{24\mathit{\_}\mathit{C}\mathit{1}a}\frac{1}{\sqrt[3]{(-216{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^{2}x+576a^3{\mathit{\_}\mathit{C}\mathit{1}}^2+12\sqrt{-\frac{49152{\mathit{\_}\mathit{C}\mathit{1}}^4{a}^7-324{\mathit{\_}\mathit{C}\mathit{1}}^4{a}^2{x}^3+1728{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^3{x}^2-1536{\mathit{\_}\mathit{C}\mathit{1}}^2{a}^{4}x-3\mathit{\_}\mathit{C}\mathit{1}{x}^3+12a{x}^2}{x}}\mathit{\_}\mathit{C}\mathit{1}a-x)x^2}}-\frac{1}{12\mathit{\_}\mathit{C}\mathit{1}a}-\frac{i}{2}\sqrt{3}(\frac{1}{12\mathit{\_}\mathit{C}\mathit{1}ax}\sqrt[3]{(-216{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^{2}x+576a^3{\mathit{\_}\mathit{C}\mathit{1}}^2+12\sqrt{-\frac{49152{\mathit{\_}\mathit{C}\mathit{1}}^4{a}^7-324{\mathit{\_}\mathit{C}\mathit{1}}^4{a}^2{x}^3+1728{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^3{x}^2-1536{\mathit{\_}\mathit{C}\mathit{1}}^2{a}^{4}x-3\mathit{\_}\mathit{C}\mathit{1}{x}^3+12a{x}^2}{x}}\mathit{\_}\mathit{C}\mathit{1}a-x)x^2}-\frac{192a^3{\mathit{\_}\mathit{C}\mathit{1}}^2+x}{12\mathit{\_}\mathit{C}\mathit{1}a}\frac{1}{\sqrt[3]{(-216{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^{2}x+576a^3{\mathit{\_}\mathit{C}\mathit{1}}^2+12\sqrt{-\frac{49152{\mathit{\_}\mathit{C}\mathit{1}}^4{a}^7-324{\mathit{\_}\mathit{C}\mathit{1}}^4{a}^2{x}^3+1728{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^3{x}^2-1536{\mathit{\_}\mathit{C}\mathit{1}}^2{a}^{4}x-3\mathit{\_}\mathit{C}\mathit{1}{x}^3+12a{x}^2}{x}}\mathit{\_}\mathit{C}\mathit{1}a-x)x^2}}),y\left(x\right)=-\frac{1}{24\mathit{\_}\mathit{C}\mathit{1}ax}\sqrt[3]{(-216{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^{2}x+576a^3{\mathit{\_}\mathit{C}\mathit{1}}^2+12\sqrt{-\frac{49152{\mathit{\_}\mathit{C}\mathit{1}}^4{a}^7-324{\mathit{\_}\mathit{C}\mathit{1}}^4{a}^2{x}^3+1728{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^3{x}^2-1536{\mathit{\_}\mathit{C}\mathit{1}}^2{a}^{4}x-3\mathit{\_}\mathit{C}\mathit{1}{x}^3+12a{x}^2}{x}}\mathit{\_}\mathit{C}\mathit{1}a-x)x^2}-\frac{192a^3{\mathit{\_}\mathit{C}\mathit{1}}^2+x}{24\mathit{\_}\mathit{C}\mathit{1}a}\frac{1}{\sqrt[3]{(-216{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^{2}x+576a^3{\mathit{\_}\mathit{C}\mathit{1}}^2+12\sqrt{-\frac{49152{\mathit{\_}\mathit{C}\mathit{1}}^4{a}^7-324{\mathit{\_}\mathit{C}\mathit{1}}^4{a}^2{x}^3+1728{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^3{x}^2-1536{\mathit{\_}\mathit{C}\mathit{1}}^2{a}^{4}x-3\mathit{\_}\mathit{C}\mathit{1}{x}^3+12a{x}^2}{x}}\mathit{\_}\mathit{C}\mathit{1}a-x)x^2}}-\frac{1}{12\mathit{\_}\mathit{C}\mathit{1}a}+\frac{i}{2}\sqrt{3}(\frac{1}{12\mathit{\_}\mathit{C}\mathit{1}ax}\sqrt[3]{(-216{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^{2}x+576a^3{\mathit{\_}\mathit{C}\mathit{1}}^2+12\sqrt{-\frac{49152{\mathit{\_}\mathit{C}\mathit{1}}^4{a}^7-324{\mathit{\_}\mathit{C}\mathit{1}}^4{a}^2{x}^3+1728{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^3{x}^2-1536{\mathit{\_}\mathit{C}\mathit{1}}^2{a}^{4}x-3\mathit{\_}\mathit{C}\mathit{1}{x}^3+12a{x}^2}{x}}\mathit{\_}\mathit{C}\mathit{1}a-x)x^2}-\frac{192a^3{\mathit{\_}\mathit{C}\mathit{1}}^2+x}{12\mathit{\_}\mathit{C}\mathit{1}a}\frac{1}{\sqrt[3]{(-216{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^{2}x+576a^3{\mathit{\_}\mathit{C}\mathit{1}}^2+12\sqrt{-\frac{49152{\mathit{\_}\mathit{C}\mathit{1}}^4{a}^7-324{\mathit{\_}\mathit{C}\mathit{1}}^4{a}^2{x}^3+1728{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^3{x}^2-1536{\mathit{\_}\mathit{C}\mathit{1}}^2{a}^{4}x-3\mathit{\_}\mathit{C}\mathit{1}{x}^3+12a{x}^2}{x}}\mathit{\_}\mathit{C}\mathit{1}a-x)x^2}})\}$$