2.290   ODE No. 290

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

$$y^{\prime }(x)(ay(x{)}^2+2bxy(x)+c{x}^2)+by(x{)}^2+2cxy(x)+d{x}^2=0$$ ✓ Mathematica : cpu = 0.314985 (sec), leaf count = 744

$$\{\{y(x)\to \frac{2^{2/3}\sqrt[3]{\sqrt{(a^2(e^{3c_1}-d{x}^3)+3abc{x}^3-2b^3{x}^3){}^2-4x^6{(b^2-ac)}^3}+a^2{e}^{3c_1}-a^{2}d{x}^3+3abc{x}^3-2b^3{x}^3}+\frac{2\sqrt[3]{2}{x}^2(b^2-ac)}{\sqrt[3]{\sqrt{(a^2(e^{3c_1}-d{x}^3)+3abc{x}^3-2b^3{x}^3){}^2-4x^6{(b^2-ac)}^3}+a^2{e}^{3c_1}-a^{2}d{x}^3+3abc{x}^3-2b^3{x}^3}}-2bx}{2a}\},\{y(x)\to \frac{9i{2}^{2/3}(\sqrt{3}+i)\sqrt[3]{\sqrt{(a^2(e^{3c_1}-d{x}^3)+3abc{x}^3-2b^3{x}^3){}^2-4x^6{(b^2-ac)}^3}+a^2{e}^{3c_1}-a^{2}d{x}^3+3abc{x}^3-2b^3{x}^3}+\frac{18\sqrt[3]{2}(1+i\sqrt{3})x^2(ac-b^2)}{\sqrt[3]{\sqrt{(a^2(e^{3c_1}-d{x}^3)+3abc{x}^3-2b^3{x}^3){}^2-4x^6{(b^2-ac)}^3}+a^2{e}^{3c_1}-a^{2}d{x}^3+3abc{x}^3-2b^3{x}^3}}-36bx}{36a}\},\{y(x)\to \frac{-92^{2/3}(1+i\sqrt{3})\sqrt[3]{\sqrt{(a^2(e^{3c_1}-d{x}^3)+3abc{x}^3-2b^3{x}^3){}^2-4x^6{(b^2-ac)}^3}+a^2{e}^{3c_1}-a^{2}d{x}^3+3abc{x}^3-2b^3{x}^3}+\frac{18i\sqrt[3]{2}(\sqrt{3}+i)x^2(b^2-ac)}{\sqrt[3]{\sqrt{(a^2(e^{3c_1}-d{x}^3)+3abc{x}^3-2b^3{x}^3){}^2-4x^6{(b^2-ac)}^3}+a^2{e}^{3c_1}-a^{2}d{x}^3+3abc{x}^3-2b^3{x}^3}}-36bx}{36a}\}\}$$

✓ Maple : cpu = 0.109 (sec), leaf count = 1388

$$\{y\left(x\right)=\frac{1}{\mathit{\_}\mathit{C}\mathit{1}}(\frac{1}{2a}\sqrt[3]{-4{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^{2}d{x}^3+12c{x}^3{\mathit{\_}\mathit{C}\mathit{1}}^{3}ba-8b^3{x}^3{\mathit{\_}\mathit{C}\mathit{1}}^3+4\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^6{a}^2{d}^2{x}^6-6{\mathit{\_}\mathit{C}\mathit{1}}^{6}abcd{x}^6+4{\mathit{\_}\mathit{C}\mathit{1}}^{6}a{c}^3{x}^6+4{\mathit{\_}\mathit{C}\mathit{1}}^6{b}^{3}d{x}^6-3{\mathit{\_}\mathit{C}\mathit{1}}^6{b}^2{c}^2{x}^6-2{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^{2}d{x}^3+6c{x}^3{\mathit{\_}\mathit{C}\mathit{1}}^{3}ba-4b^3{x}^3{\mathit{\_}\mathit{C}\mathit{1}}^3+a^2}a+4a^2}-2\frac{{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2(ac-b^2)}{a\sqrt[3]{-4{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^{2}d{x}^3+12c{x}^3{\mathit{\_}\mathit{C}\mathit{1}}^{3}ba-8b^3{x}^3{\mathit{\_}\mathit{C}\mathit{1}}^3+4\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^6{a}^2{d}^2{x}^6-6{\mathit{\_}\mathit{C}\mathit{1}}^{6}abcd{x}^6+4{\mathit{\_}\mathit{C}\mathit{1}}^{6}a{c}^3{x}^6+4{\mathit{\_}\mathit{C}\mathit{1}}^6{b}^{3}d{x}^6-3{\mathit{\_}\mathit{C}\mathit{1}}^6{b}^2{c}^2{x}^6-2{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^{2}d{x}^3+6c{x}^3{\mathit{\_}\mathit{C}\mathit{1}}^{3}ba-4b^3{x}^3{\mathit{\_}\mathit{C}\mathit{1}}^3+a^2}a+4a^2}}-\frac{bx\mathit{\_}\mathit{C}\mathit{1}}{a}),y\left(x\right)=\frac{1}{4a\mathit{\_}\mathit{C}\mathit{1}}(-4bx\mathit{\_}\mathit{C}\mathit{1}\sqrt[3]{4\sqrt{(a^2{d}^2+(-6bcd+4c^3)a+4b^{3}d-3b^2{c}^2)x^6{\mathit{\_}\mathit{C}\mathit{1}}^6-2x^3(a^{2}d-3abc+2b^3){\mathit{\_}\mathit{C}\mathit{1}}^3+a^2}a+(-4{\mathit{\_}\mathit{C}\mathit{1}}^{3}d{x}^3+4)a^2+12c{x}^3{\mathit{\_}\mathit{C}\mathit{1}}^{3}ba-8b^3{x}^3{\mathit{\_}\mathit{C}\mathit{1}}^3}+(4i(ac-b^2)x^2{\mathit{\_}\mathit{C}\mathit{1}}^2+i{(-4{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^{2}d{x}^3+12c{x}^3{\mathit{\_}\mathit{C}\mathit{1}}^{3}ba-8b^3{x}^3{\mathit{\_}\mathit{C}\mathit{1}}^3+4\sqrt{(a^2{d}^2+(-6bcd+4c^3)a+4b^{3}d-3b^2{c}^2)x^6{\mathit{\_}\mathit{C}\mathit{1}}^6-2x^3(a^{2}d-3abc+2b^3){\mathit{\_}\mathit{C}\mathit{1}}^3+a^2}a+4a^2)}^{\frac{2}{3}})\sqrt{3}+4{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2(ac-b^2)-{(-4{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^{2}d{x}^3+12c{x}^3{\mathit{\_}\mathit{C}\mathit{1}}^{3}ba-8b^3{x}^3{\mathit{\_}\mathit{C}\mathit{1}}^3+4\sqrt{(a^2{d}^2+(-6bcd+4c^3)a+4b^{3}d-3b^2{c}^2)x^6{\mathit{\_}\mathit{C}\mathit{1}}^6-2x^3(a^{2}d-3abc+2b^3){\mathit{\_}\mathit{C}\mathit{1}}^3+a^2}a+4a^2)}^{\frac{2}{3}})\frac{1}{\sqrt[3]{4\sqrt{(a^2{d}^2+(-6bcd+4c^3)a+4b^{3}d-3b^2{c}^2)x^6{\mathit{\_}\mathit{C}\mathit{1}}^6-2x^3(a^{2}d-3abc+2b^3){\mathit{\_}\mathit{C}\mathit{1}}^3+a^2}a+(-4{\mathit{\_}\mathit{C}\mathit{1}}^{3}d{x}^3+4)a^2+12c{x}^3{\mathit{\_}\mathit{C}\mathit{1}}^{3}ba-8b^3{x}^3{\mathit{\_}\mathit{C}\mathit{1}}^3}},y\left(x\right)=-\frac{1}{4a\mathit{\_}\mathit{C}\mathit{1}}(4bx\mathit{\_}\mathit{C}\mathit{1}\sqrt[3]{4\sqrt{(a^2{d}^2+(-6bcd+4c^3)a+4b^{3}d-3b^2{c}^2)x^6{\mathit{\_}\mathit{C}\mathit{1}}^6-2x^3(a^{2}d-3abc+2b^3){\mathit{\_}\mathit{C}\mathit{1}}^3+a^2}a+(-4{\mathit{\_}\mathit{C}\mathit{1}}^{3}d{x}^3+4)a^2+12c{x}^3{\mathit{\_}\mathit{C}\mathit{1}}^{3}ba-8b^3{x}^3{\mathit{\_}\mathit{C}\mathit{1}}^3}+(4i(ac-b^2)x^2{\mathit{\_}\mathit{C}\mathit{1}}^2+i{(-4{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^{2}d{x}^3+12c{x}^3{\mathit{\_}\mathit{C}\mathit{1}}^{3}ba-8b^3{x}^3{\mathit{\_}\mathit{C}\mathit{1}}^3+4\sqrt{(a^2{d}^2+(-6bcd+4c^3)a+4b^{3}d-3b^2{c}^2)x^6{\mathit{\_}\mathit{C}\mathit{1}}^6-2x^3(a^{2}d-3abc+2b^3){\mathit{\_}\mathit{C}\mathit{1}}^3+a^2}a+4a^2)}^{\frac{2}{3}})\sqrt{3}-4{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2(ac-b^2)+{(-4{\mathit{\_}\mathit{C}\mathit{1}}^3{a}^{2}d{x}^3+12c{x}^3{\mathit{\_}\mathit{C}\mathit{1}}^{3}ba-8b^3{x}^3{\mathit{\_}\mathit{C}\mathit{1}}^3+4\sqrt{(a^2{d}^2+(-6bcd+4c^3)a+4b^{3}d-3b^2{c}^2)x^6{\mathit{\_}\mathit{C}\mathit{1}}^6-2x^3(a^{2}d-3abc+2b^3){\mathit{\_}\mathit{C}\mathit{1}}^3+a^2}a+4a^2)}^{\frac{2}{3}})\frac{1}{\sqrt[3]{4\sqrt{(a^2{d}^2+(-6bcd+4c^3)a+4b^{3}d-3b^2{c}^2)x^6{\mathit{\_}\mathit{C}\mathit{1}}^6-2x^3(a^{2}d-3abc+2b^3){\mathit{\_}\mathit{C}\mathit{1}}^3+a^2}a+(-4{\mathit{\_}\mathit{C}\mathit{1}}^{3}d{x}^3+4)a^2+12c{x}^3{\mathit{\_}\mathit{C}\mathit{1}}^{3}ba-8b^3{x}^3{\mathit{\_}\mathit{C}\mathit{1}}^3}}\}$$