2.323   ODE No. 323

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

$$\text{Global}\stackrel{`}{}\text{x}{\text{Global}\stackrel{`}{}\text{y}}^{\prime }(\text{Global}\stackrel{`}{}\text{x})(\text{Global}\stackrel{`}{}\text{a}\text{Global}\stackrel{`}{}\text{x}\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x}{)}^3+\text{Global}\stackrel{`}{}\text{c})+\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})(\text{Global}\stackrel{`}{}\text{b}{\text{Global}\stackrel{`}{}\text{x}}^3\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})+\text{Global}\stackrel{`}{}\text{c})=0$$ ✓ Mathematica : cpu = 0.0491124 (sec), leaf count = 463

$$\{\{\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})\to \frac{\sqrt[3]{\sqrt{108{\text{Global}\stackrel{`}{}\text{a}}^3{\text{Global}\stackrel{`}{}\text{x}}^3(\text{Global}\stackrel{`}{}\text{b}{\text{Global}\stackrel{`}{}\text{x}}^3-2c_1\text{Global}\stackrel{`}{}\text{x}){}^3+2916{\text{Global}\stackrel{`}{}\text{a}}^4{\text{Global}\stackrel{`}{}\text{c}}^2{\text{Global}\stackrel{`}{}\text{x}}^4}+54{\text{Global}\stackrel{`}{}\text{a}}^2\text{Global}\stackrel{`}{}\text{c}{\text{Global}\stackrel{`}{}\text{x}}^2}}{3\sqrt[3]{2}\text{Global}\stackrel{`}{}\text{a}\text{Global}\stackrel{`}{}\text{x}}-\frac{\sqrt[3]{2}(\text{Global}\stackrel{`}{}\text{b}{\text{Global}\stackrel{`}{}\text{x}}^3-2c_1\text{Global}\stackrel{`}{}\text{x})}{\sqrt[3]{\sqrt{108{\text{Global}\stackrel{`}{}\text{a}}^3{\text{Global}\stackrel{`}{}\text{x}}^3(\text{Global}\stackrel{`}{}\text{b}{\text{Global}\stackrel{`}{}\text{x}}^3-2c_1\text{Global}\stackrel{`}{}\text{x}){}^3+2916{\text{Global}\stackrel{`}{}\text{a}}^4{\text{Global}\stackrel{`}{}\text{c}}^2{\text{Global}\stackrel{`}{}\text{x}}^4}+54{\text{Global}\stackrel{`}{}\text{a}}^2\text{Global}\stackrel{`}{}\text{c}{\text{Global}\stackrel{`}{}\text{x}}^2}}\},\{\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})\to \frac{(1+i\sqrt{3})(\text{Global}\stackrel{`}{}\text{b}{\text{Global}\stackrel{`}{}\text{x}}^3-2c_1\text{Global}\stackrel{`}{}\text{x})}{2^{2/3}\sqrt[3]{\sqrt{108{\text{Global}\stackrel{`}{}\text{a}}^3{\text{Global}\stackrel{`}{}\text{x}}^3(\text{Global}\stackrel{`}{}\text{b}{\text{Global}\stackrel{`}{}\text{x}}^3-2c_1\text{Global}\stackrel{`}{}\text{x}){}^3+2916{\text{Global}\stackrel{`}{}\text{a}}^4{\text{Global}\stackrel{`}{}\text{c}}^2{\text{Global}\stackrel{`}{}\text{x}}^4}+54{\text{Global}\stackrel{`}{}\text{a}}^2\text{Global}\stackrel{`}{}\text{c}{\text{Global}\stackrel{`}{}\text{x}}^2}}-\frac{(1-i\sqrt{3})\sqrt[3]{\sqrt{108{\text{Global}\stackrel{`}{}\text{a}}^3{\text{Global}\stackrel{`}{}\text{x}}^3(\text{Global}\stackrel{`}{}\text{b}{\text{Global}\stackrel{`}{}\text{x}}^3-2c_1\text{Global}\stackrel{`}{}\text{x}){}^3+2916{\text{Global}\stackrel{`}{}\text{a}}^4{\text{Global}\stackrel{`}{}\text{c}}^2{\text{Global}\stackrel{`}{}\text{x}}^4}+54{\text{Global}\stackrel{`}{}\text{a}}^2\text{Global}\stackrel{`}{}\text{c}{\text{Global}\stackrel{`}{}\text{x}}^2}}{6\sqrt[3]{2}\text{Global}\stackrel{`}{}\text{a}\text{Global}\stackrel{`}{}\text{x}}\},\{\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})\to \frac{(1-i\sqrt{3})(\text{Global}\stackrel{`}{}\text{b}{\text{Global}\stackrel{`}{}\text{x}}^3-2c_1\text{Global}\stackrel{`}{}\text{x})}{2^{2/3}\sqrt[3]{\sqrt{108{\text{Global}\stackrel{`}{}\text{a}}^3{\text{Global}\stackrel{`}{}\text{x}}^3(\text{Global}\stackrel{`}{}\text{b}{\text{Global}\stackrel{`}{}\text{x}}^3-2c_1\text{Global}\stackrel{`}{}\text{x}){}^3+2916{\text{Global}\stackrel{`}{}\text{a}}^4{\text{Global}\stackrel{`}{}\text{c}}^2{\text{Global}\stackrel{`}{}\text{x}}^4}+54{\text{Global}\stackrel{`}{}\text{a}}^2\text{Global}\stackrel{`}{}\text{c}{\text{Global}\stackrel{`}{}\text{x}}^2}}-\frac{(1+i\sqrt{3})\sqrt[3]{\sqrt{108{\text{Global}\stackrel{`}{}\text{a}}^3{\text{Global}\stackrel{`}{}\text{x}}^3(\text{Global}\stackrel{`}{}\text{b}{\text{Global}\stackrel{`}{}\text{x}}^3-2c_1\text{Global}\stackrel{`}{}\text{x}){}^3+2916{\text{Global}\stackrel{`}{}\text{a}}^4{\text{Global}\stackrel{`}{}\text{c}}^2{\text{Global}\stackrel{`}{}\text{x}}^4}+54{\text{Global}\stackrel{`}{}\text{a}}^2\text{Global}\stackrel{`}{}\text{c}{\text{Global}\stackrel{`}{}\text{x}}^2}}{6\sqrt[3]{2}\text{Global}\stackrel{`}{}\text{a}\text{Global}\stackrel{`}{}\text{x}}\}\}$$

✓ Maple : cpu = 0.134 (sec), leaf count = 761

$$\{y\left(x\right)=\frac{1}{3ax}\sqrt[3]{(27c+3\sqrt{-3\frac{-b^3{x}^8+6\mathit{\_}\mathit{C}\mathit{1}{b}^2{x}^6-12{\mathit{\_}\mathit{C}\mathit{1}}^{2}b{x}^4+8{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^2-27c^{2}a}{a}})a^2{x}^2}+x(-b{x}^2+2\mathit{\_}\mathit{C}\mathit{1})\frac{1}{\sqrt[3]{(27c+3\sqrt{-3\frac{-b^3{x}^8+6\mathit{\_}\mathit{C}\mathit{1}{b}^2{x}^6-12{\mathit{\_}\mathit{C}\mathit{1}}^{2}b{x}^4+8{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^2-27c^{2}a}{a}})a^2{x}^2}},y\left(x\right)=-\frac{1}{6ax}\sqrt[3]{(27c+3\sqrt{-3\frac{-b^3{x}^8+6\mathit{\_}\mathit{C}\mathit{1}{b}^2{x}^6-12{\mathit{\_}\mathit{C}\mathit{1}}^{2}b{x}^4+8{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^2-27c^{2}a}{a}})a^2{x}^2}-\frac{x(-b{x}^2+2\mathit{\_}\mathit{C}\mathit{1})}{2}\frac{1}{\sqrt[3]{(27c+3\sqrt{-3\frac{-b^3{x}^8+6\mathit{\_}\mathit{C}\mathit{1}{b}^2{x}^6-12{\mathit{\_}\mathit{C}\mathit{1}}^{2}b{x}^4+8{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^2-27c^{2}a}{a}})a^2{x}^2}}-\frac{i}{2}\sqrt{3}(\frac{1}{3ax}\sqrt[3]{(27c+3\sqrt{-3\frac{-b^3{x}^8+6\mathit{\_}\mathit{C}\mathit{1}{b}^2{x}^6-12{\mathit{\_}\mathit{C}\mathit{1}}^{2}b{x}^4+8{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^2-27c^{2}a}{a}})a^2{x}^2}-x(-b{x}^2+2\mathit{\_}\mathit{C}\mathit{1})\frac{1}{\sqrt[3]{(27c+3\sqrt{-3\frac{-b^3{x}^8+6\mathit{\_}\mathit{C}\mathit{1}{b}^2{x}^6-12{\mathit{\_}\mathit{C}\mathit{1}}^{2}b{x}^4+8{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^2-27c^{2}a}{a}})a^2{x}^2}}),y\left(x\right)=-\frac{1}{6ax}\sqrt[3]{(27c+3\sqrt{-3\frac{-b^3{x}^8+6\mathit{\_}\mathit{C}\mathit{1}{b}^2{x}^6-12{\mathit{\_}\mathit{C}\mathit{1}}^{2}b{x}^4+8{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^2-27c^{2}a}{a}})a^2{x}^2}-\frac{x(-b{x}^2+2\mathit{\_}\mathit{C}\mathit{1})}{2}\frac{1}{\sqrt[3]{(27c+3\sqrt{-3\frac{-b^3{x}^8+6\mathit{\_}\mathit{C}\mathit{1}{b}^2{x}^6-12{\mathit{\_}\mathit{C}\mathit{1}}^{2}b{x}^4+8{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^2-27c^{2}a}{a}})a^2{x}^2}}+\frac{i}{2}\sqrt{3}(\frac{1}{3ax}\sqrt[3]{(27c+3\sqrt{-3\frac{-b^3{x}^8+6\mathit{\_}\mathit{C}\mathit{1}{b}^2{x}^6-12{\mathit{\_}\mathit{C}\mathit{1}}^{2}b{x}^4+8{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^2-27c^{2}a}{a}})a^2{x}^2}-x(-b{x}^2+2\mathit{\_}\mathit{C}\mathit{1})\frac{1}{\sqrt[3]{(27c+3\sqrt{-3\frac{-b^3{x}^8+6\mathit{\_}\mathit{C}\mathit{1}{b}^2{x}^6-12{\mathit{\_}\mathit{C}\mathit{1}}^{2}b{x}^4+8{\mathit{\_}\mathit{C}\mathit{1}}^3{x}^2-27c^{2}a}{a}})a^2{x}^2}})\}$$