2.738   ODE No. 738

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

$$y^{\prime }(x)=\frac{2a}{32a^3-16a^{2}xy(x{)}^2+2a{x}^{2}y(x{)}^4-x^{2}y(x)}$$ ✓ Mathematica : cpu = 0.561394 (sec), leaf count = 1200

$$\{\{y(x)\to \frac{-2(4a+e^{c_1})+\frac{2\sqrt[3]{2304x^2{a}^4-64x^3{a}^3+576e^{c_1}{x}^2{a}^3-48e^{c_1}{x}^3{a}^2-216x^3{a}^2-12e^{2c_1}{x}^{3}a-e^{3c_1}{x}^3+\sqrt{x^3(x(-2304a^4-64(9e^{c_1}-x)a^3+24(9+2e^{c_1})x{a}^2+12e^{2c_1}xa+e^{3c_1}x){}^2-(192a^3+(4a+e^{c_1}){}^{2}x){}^3)}}}{x}+\frac{2(192a^3+16x{a}^2+8e^{c_1}xa+e^{2c_1}x)}{\sqrt[3]{2304x^2{a}^4-64x^3{a}^3+576e^{c_1}{x}^2{a}^3-48e^{c_1}{x}^3{a}^2-216x^3{a}^2-12e^{2c_1}{x}^{3}a-e^{3c_1}{x}^3+\sqrt{x^3(x(-2304a^4-64(9e^{c_1}-x)a^3+24(9+2e^{c_1})x{a}^2+12e^{2c_1}xa+e^{3c_1}x){}^2-(192a^3+(4a+e^{c_1}){}^{2}x){}^3)}}}}{24a}\},\{y(x)\to \frac{-4(4a+e^{c_1})+\frac{2i(i+\sqrt{3})\sqrt[3]{2304x^2{a}^4-64x^3{a}^3+576e^{c_1}{x}^2{a}^3-48e^{c_1}{x}^3{a}^2-216x^3{a}^2-12e^{2c_1}{x}^{3}a-e^{3c_1}{x}^3+\sqrt{x^3(x(-2304a^4-64(9e^{c_1}-x)a^3+24(9+2e^{c_1})x{a}^2+12e^{2c_1}xa+e^{3c_1}x){}^2-(192a^3+(4a+e^{c_1}){}^{2}x){}^3)}}}{x}-\frac{2i(-i+\sqrt{3})(192a^3+16x{a}^2+8e^{c_1}xa+e^{2c_1}x)}{\sqrt[3]{2304x^2{a}^4-64x^3{a}^3+576e^{c_1}{x}^2{a}^3-48e^{c_1}{x}^3{a}^2-216x^3{a}^2-12e^{2c_1}{x}^{3}a-e^{3c_1}{x}^3+\sqrt{x^3(x(-2304a^4-64(9e^{c_1}-x)a^3+24(9+2e^{c_1})x{a}^2+12e^{2c_1}xa+e^{3c_1}x){}^2-(192a^3+(4a+e^{c_1}){}^{2}x){}^3)}}}}{48a}\},\{y(x)\to \frac{-4(4a+e^{c_1})-\frac{2i(-i+\sqrt{3})\sqrt[3]{2304x^2{a}^4-64x^3{a}^3+576e^{c_1}{x}^2{a}^3-48e^{c_1}{x}^3{a}^2-216x^3{a}^2-12e^{2c_1}{x}^{3}a-e^{3c_1}{x}^3+\sqrt{x^3(x(-2304a^4-64(9e^{c_1}-x)a^3+24(9+2e^{c_1})x{a}^2+12e^{2c_1}xa+e^{3c_1}x){}^2-(192a^3+(4a+e^{c_1}){}^{2}x){}^3)}}}{x}+\frac{2i(i+\sqrt{3})(192a^3+16x{a}^2+8e^{c_1}xa+e^{2c_1}x)}{\sqrt[3]{2304x^2{a}^4-64x^3{a}^3+576e^{c_1}{x}^2{a}^3-48e^{c_1}{x}^3{a}^2-216x^3{a}^2-12e^{2c_1}{x}^{3}a-e^{3c_1}{x}^3+\sqrt{x^3(x(-2304a^4-64(9e^{c_1}-x)a^3+24(9+2e^{c_1})x{a}^2+12e^{2c_1}xa+e^{3c_1}x){}^2-(192a^3+(4a+e^{c_1}){}^{2}x){}^3)}}}}{48a}\}\}$$

✓ Maple : cpu = 0.816 (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}\}$$