3.290   ODE No. 290

$$\boxed{{\displaystyle (a{\left(y\left(x\right)\right)}^2+2bxy\left(x\right)+c{x}^2)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+b{\left(y\left(x\right)\right)}^2+2cxy\left(x\right)+d{x}^2=0}}$$

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

Mathematica: cpu = 0.056007 (sec), leaf count = 831 $$\{\{y(x)\to -\frac{bx}{a}+\frac{\sqrt[3]{-54b^3{x}^3+81abc{x}^3-27a^{2}d{x}^3+27a^2{e}^{3c_1}+\sqrt{4{(9ac{x}^2-9b^2{x}^2)}^3+(-54b^3{x}^3+81abc{x}^3-27a^{2}d{x}^3+27a^2{e}^{3c_1}){}^2}}}{3\sqrt[3]{2}a}-\frac{\sqrt[3]{2}(9ac{x}^2-9b^2{x}^2)}{3a\sqrt[3]{-54b^3{x}^3+81abc{x}^3-27a^{2}d{x}^3+27a^2{e}^{3c_1}+\sqrt{4{(9ac{x}^2-9b^2{x}^2)}^3+(-54b^3{x}^3+81abc{x}^3-27a^{2}d{x}^3+27a^2{e}^{3c_1}){}^2}}}\},\{y(x)\to -\frac{bx}{a}-\frac{(1-i\sqrt{3})\sqrt[3]{-54b^3{x}^3+81abc{x}^3-27a^{2}d{x}^3+27a^2{e}^{3c_1}+\sqrt{4{(9ac{x}^2-9b^2{x}^2)}^3+(-54b^3{x}^3+81abc{x}^3-27a^{2}d{x}^3+27a^2{e}^{3c_1}){}^2}}}{6\sqrt[3]{2}a}+\frac{(1+i\sqrt{3})(9ac{x}^2-9b^2{x}^2)}{32^{2/3}a\sqrt[3]{-54b^3{x}^3+81abc{x}^3-27a^{2}d{x}^3+27a^2{e}^{3c_1}+\sqrt{4{(9ac{x}^2-9b^2{x}^2)}^3+(-54b^3{x}^3+81abc{x}^3-27a^{2}d{x}^3+27a^2{e}^{3c_1}){}^2}}}\},\{y(x)\to -\frac{bx}{a}-\frac{(1+i\sqrt{3})\sqrt[3]{-54b^3{x}^3+81abc{x}^3-27a^{2}d{x}^3+27a^2{e}^{3c_1}+\sqrt{4{(9ac{x}^2-9b^2{x}^2)}^3+(-54b^3{x}^3+81abc{x}^3-27a^{2}d{x}^3+27a^2{e}^{3c_1}){}^2}}}{6\sqrt[3]{2}a}+\frac{(1-i\sqrt{3})(9ac{x}^2-9b^2{x}^2)}{32^{2/3}a\sqrt[3]{-54b^3{x}^3+81abc{x}^3-27a^{2}d{x}^3+27a^2{e}^{3c_1}+\sqrt{4{(9ac{x}^2-9b^2{x}^2)}^3+(-54b^3{x}^3+81abc{x}^3-27a^{2}d{x}^3+27a^2{e}^{3c_1}){}^2}}}\}\}$$

Maple: cpu = 0.062 (sec), leaf count = 1666 $$\{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}{\mathit{\_}\mathit{C}\mathit{1}}(-\frac{1}{4a}\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{{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2(ac-b^2)}{a}\frac{1}{\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}-\frac{i}{2}\sqrt{3}(\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}})),y\left(x\right)=\frac{1}{\mathit{\_}\mathit{C}\mathit{1}}(-\frac{1}{4a}\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{{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2(ac-b^2)}{a}\frac{1}{\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}+\frac{i}{2}\sqrt{3}(\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}}))\}$$