2.738   ODE No. 738

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

$$y^{\prime }(x)=\frac{2a}{-16a^{2}xy(x{)}^2+32a^3+2a{x}^{2}y(x{)}^4-x^{2}y(x)}$$ ✓ Mathematica : cpu = 0.468192 (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 = 0.869 (sec), leaf count = 1054

$$\{y\left(x\right)=\frac{1}{24\mathit{\_}\mathit{C}\mathit{1}ax}(-2x\sqrt[3]{-216{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^2{x}^3+576{\mathit{\_}\mathit{C}\mathit{1}}^2{a}^3{x}^2+12a\mathit{\_}\mathit{C}\mathit{1}{x}^2\sqrt{\frac{(324{\mathit{\_}\mathit{C}\mathit{1}}^4{a}^2+3\mathit{\_}\mathit{C}\mathit{1})x^3+(-1728{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^3-12a)x^2+1536{\mathit{\_}\mathit{C}\mathit{1}}^2{a}^{4}x-49152{\mathit{\_}\mathit{C}\mathit{1}}^4{a}^7}{x}}-x^3}+(-192i{\mathit{\_}\mathit{C}\mathit{1}}^2{a}^{3}x+i{\left((-216{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^{2}x+576a^3{\mathit{\_}\mathit{C}\mathit{1}}^2+12\sqrt{\frac{(324{\mathit{\_}\mathit{C}\mathit{1}}^4{a}^2+3\mathit{\_}\mathit{C}\mathit{1})x^3+(-1728{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^3-12a)x^2+1536{\mathit{\_}\mathit{C}\mathit{1}}^2{a}^{4}x-49152{\mathit{\_}\mathit{C}\mathit{1}}^4{a}^7}{x}}\mathit{\_}\mathit{C}\mathit{1}a-x)x^2\right)}^{\frac{2}{3}}-i{x}^2)\sqrt{3}-192{\mathit{\_}\mathit{C}\mathit{1}}^2{a}^{3}x-{\left((-216{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^{2}x+576a^3{\mathit{\_}\mathit{C}\mathit{1}}^2+12\sqrt{\frac{(324{\mathit{\_}\mathit{C}\mathit{1}}^4{a}^2+3\mathit{\_}\mathit{C}\mathit{1})x^3+(-1728{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^3-12a)x^2+1536{\mathit{\_}\mathit{C}\mathit{1}}^2{a}^{4}x-49152{\mathit{\_}\mathit{C}\mathit{1}}^4{a}^7}{x}}\mathit{\_}\mathit{C}\mathit{1}a-x)x^2\right)}^{\frac{2}{3}}-x^2)\frac{1}{\sqrt[3]{-216{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^2{x}^3+576{\mathit{\_}\mathit{C}\mathit{1}}^2{a}^3{x}^2+12a\mathit{\_}\mathit{C}\mathit{1}{x}^2\sqrt{\frac{(324{\mathit{\_}\mathit{C}\mathit{1}}^4{a}^2+3\mathit{\_}\mathit{C}\mathit{1})x^3+(-1728{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^3-12a)x^2+1536{\mathit{\_}\mathit{C}\mathit{1}}^2{a}^{4}x-49152{\mathit{\_}\mathit{C}\mathit{1}}^4{a}^7}{x}}-x^3}},y\left(x\right)=-\frac{1}{24\mathit{\_}\mathit{C}\mathit{1}ax}(2x\sqrt[3]{-216{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^2{x}^3+576{\mathit{\_}\mathit{C}\mathit{1}}^2{a}^3{x}^2+12a\mathit{\_}\mathit{C}\mathit{1}{x}^2\sqrt{\frac{(324{\mathit{\_}\mathit{C}\mathit{1}}^4{a}^2+3\mathit{\_}\mathit{C}\mathit{1})x^3+(-1728{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^3-12a)x^2+1536{\mathit{\_}\mathit{C}\mathit{1}}^2{a}^{4}x-49152{\mathit{\_}\mathit{C}\mathit{1}}^4{a}^7}{x}}-x^3}+(-192i{\mathit{\_}\mathit{C}\mathit{1}}^2{a}^{3}x+i{\left((-216{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^{2}x+576a^3{\mathit{\_}\mathit{C}\mathit{1}}^2+12\sqrt{\frac{(324{\mathit{\_}\mathit{C}\mathit{1}}^4{a}^2+3\mathit{\_}\mathit{C}\mathit{1})x^3+(-1728{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^3-12a)x^2+1536{\mathit{\_}\mathit{C}\mathit{1}}^2{a}^{4}x-49152{\mathit{\_}\mathit{C}\mathit{1}}^4{a}^7}{x}}\mathit{\_}\mathit{C}\mathit{1}a-x)x^2\right)}^{\frac{2}{3}}-i{x}^2)\sqrt{3}+192{\mathit{\_}\mathit{C}\mathit{1}}^2{a}^{3}x+{\left((-216{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^{2}x+576a^3{\mathit{\_}\mathit{C}\mathit{1}}^2+12\sqrt{\frac{(324{\mathit{\_}\mathit{C}\mathit{1}}^4{a}^2+3\mathit{\_}\mathit{C}\mathit{1})x^3+(-1728{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^3-12a)x^2+1536{\mathit{\_}\mathit{C}\mathit{1}}^2{a}^{4}x-49152{\mathit{\_}\mathit{C}\mathit{1}}^4{a}^7}{x}}\mathit{\_}\mathit{C}\mathit{1}a-x)x^2\right)}^{\frac{2}{3}}+x^2)\frac{1}{\sqrt[3]{-216{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^2{x}^3+576{\mathit{\_}\mathit{C}\mathit{1}}^2{a}^3{x}^2+12a\mathit{\_}\mathit{C}\mathit{1}{x}^2\sqrt{\frac{(324{\mathit{\_}\mathit{C}\mathit{1}}^4{a}^2+3\mathit{\_}\mathit{C}\mathit{1})x^3+(-1728{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^3-12a)x^2+1536{\mathit{\_}\mathit{C}\mathit{1}}^2{a}^{4}x-49152{\mathit{\_}\mathit{C}\mathit{1}}^4{a}^7}{x}}-x^3}},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{-3\frac{16384{\mathit{\_}\mathit{C}\mathit{1}}^4{a}^7-108{\mathit{\_}\mathit{C}\mathit{1}}^4{a}^2{x}^3+576{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^3{x}^2-512{\mathit{\_}\mathit{C}\mathit{1}}^2{a}^{4}x-\mathit{\_}\mathit{C}\mathit{1}{x}^3+4a{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{-3\frac{16384{\mathit{\_}\mathit{C}\mathit{1}}^4{a}^7-108{\mathit{\_}\mathit{C}\mathit{1}}^4{a}^2{x}^3+576{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^3{x}^2-512{\mathit{\_}\mathit{C}\mathit{1}}^2{a}^{4}x-\mathit{\_}\mathit{C}\mathit{1}{x}^3+4a{x}^2}{x}}\mathit{\_}\mathit{C}\mathit{1}a-x)x^2}}-\frac{1}{12\mathit{\_}\mathit{C}\mathit{1}a}\}$$