2.323   ODE No. 323

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

$$x{y}^{\prime }(x)(axy(x{)}^3+c)+y(x)(b{x}^{3}y(x)+c)=0$$ ✓ Mathematica : cpu = 0.050313 (sec), leaf count = 484

$$\{\{y(x)\to \frac{x(2c_1-b{x}^2)}{\sqrt[3]{3}\sqrt[3]{\sqrt{3}\sqrt{a^3{x}^4(27a{c}^2+x^2(b{x}^2-2c_1){}^3)}+9a^{2}c{x}^2}}+\frac{\sqrt[3]{\sqrt{3}\sqrt{a^3{x}^4(27a{c}^2+x^2(b{x}^2-2c_1){}^3)}+9a^{2}c{x}^2}}{3^{2/3}ax}\},\{y(x)\to \frac{i\sqrt[3]{3}(\sqrt{3}+i)(\sqrt{3}\sqrt{a^3{x}^4(27a{c}^2+x^2(b{x}^2-2c_1){}^3)}+9a^{2}c{x}^2){}^{2/3}+\sqrt[6]{3}(\sqrt{3}+3i)a{x}^2(b{x}^2-2c_1)}{6ax\sqrt[3]{\sqrt{3}\sqrt{a^3{x}^4(27a{c}^2+x^2(b{x}^2-2c_1){}^3)}+9a^{2}c{x}^2}}\},\{y(x)\to \frac{\sqrt[6]{3}(\sqrt{3}-3i)a{x}^2(b{x}^2-2c_1)-i\sqrt[3]{3}(\sqrt{3}-i)(\sqrt{3}\sqrt{a^3{x}^4(27a{c}^2+x^2(b{x}^2-2c_1){}^3)}+9a^{2}c{x}^2){}^{2/3}}{6ax\sqrt[3]{\sqrt{3}\sqrt{a^3{x}^4(27a{c}^2+x^2(b{x}^2-2c_1){}^3)}+9a^{2}c{x}^2}}\}\}$$

✓ Maple : cpu = 0.143 (sec), leaf count = 630

$$\{y\left(x\right)=-\frac{3^{\frac{2}{3}}}{18ax}((3i(b{x}^2-2\mathit{\_}\mathit{C}\mathit{1})x^{2}a+i{\left((27c+3\sqrt{\frac{3b^3{x}^8-18\mathit{\_}\mathit{C}\mathit{1}{b}^2{x}^6+36{\mathit{\_}\mathit{C}\mathit{1}}^{2}b{x}^4-24{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^2+81c^{2}a}{a}})a^2{x}^2\right)}^{\frac{2}{3}})\sqrt{3}+(-3x^{4}b+6x^2\mathit{\_}\mathit{C}\mathit{1})a+{\left((27c+3\sqrt{\frac{3b^3{x}^8-18\mathit{\_}\mathit{C}\mathit{1}{b}^2{x}^6+36{\mathit{\_}\mathit{C}\mathit{1}}^{2}b{x}^4-24{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^2+81c^{2}a}{a}})a^2{x}^2\right)}^{\frac{2}{3}})\frac{1}{\sqrt[3]{(9c+\sqrt{\frac{3b^3{x}^8-18\mathit{\_}\mathit{C}\mathit{1}{b}^2{x}^6+36{\mathit{\_}\mathit{C}\mathit{1}}^{2}b{x}^4-24{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^2+81c^{2}a}{a}})a^2{x}^2}},y\left(x\right)=\frac{3^{\frac{2}{3}}}{18ax}((3i(b{x}^2-2\mathit{\_}\mathit{C}\mathit{1})x^{2}a+i{\left((27c+3\sqrt{\frac{3b^3{x}^8-18\mathit{\_}\mathit{C}\mathit{1}{b}^2{x}^6+36{\mathit{\_}\mathit{C}\mathit{1}}^{2}b{x}^4-24{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^2+81c^{2}a}{a}})a^2{x}^2\right)}^{\frac{2}{3}})\sqrt{3}+(3x^{4}b-6x^2\mathit{\_}\mathit{C}\mathit{1})a-{\left((27c+3\sqrt{\frac{3b^3{x}^8-18\mathit{\_}\mathit{C}\mathit{1}{b}^2{x}^6+36{\mathit{\_}\mathit{C}\mathit{1}}^{2}b{x}^4-24{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^2+81c^{2}a}{a}})a^2{x}^2\right)}^{\frac{2}{3}})\frac{1}{\sqrt[3]{(9c+\sqrt{\frac{3b^3{x}^8-18\mathit{\_}\mathit{C}\mathit{1}{b}^2{x}^6+36{\mathit{\_}\mathit{C}\mathit{1}}^{2}b{x}^4-24{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^2+81c^{2}a}{a}})a^2{x}^2}},y\left(x\right)=\frac{3^{\frac{2}{3}}}{9ax}(-3ab{x}^4+6\mathit{\_}\mathit{C}\mathit{1}a{x}^2+{\left((27c+3\sqrt{\frac{3b^3{x}^8-18\mathit{\_}\mathit{C}\mathit{1}{b}^2{x}^6+36{\mathit{\_}\mathit{C}\mathit{1}}^{2}b{x}^4-24{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^2+81c^{2}a}{a}})a^2{x}^2\right)}^{\frac{2}{3}})\frac{1}{\sqrt[3]{(9c+\sqrt{\frac{3b^3{x}^8-18\mathit{\_}\mathit{C}\mathit{1}{b}^2{x}^6+36{\mathit{\_}\mathit{C}\mathit{1}}^{2}b{x}^4-24{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^2+81c^{2}a}{a}})a^2{x}^2}}\}$$