3.726   ODE No. 726

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=-\frac{by\left(x\right)a-bc+b^{2}x+ba\sqrt{x}-a^2}{a(ay\left(x\right)-c+bx+a\sqrt{x})}=0}}$$

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

Mathematica: cpu = 0.082010 (sec), leaf count = 625 $$\{\{y(x)\to \frac{1}{a^2\text{Root}[{\mathrm{\#}\text{1}}^6(16e^{12c_1}+16x^3)-\frac{24{\mathrm{\#}\text{1}}^4{x}^2}{a^4}+\frac{8{\mathrm{\#}\text{1}}^3{x}^{3/2}}{a^6}+\frac{9{\mathrm{\#}\text{1}}^{2}x}{a^8}-\frac{6\mathrm{\#}\text{1}\sqrt{x}}{a^{10}}+\frac{1}{a^{12}}\mathrm{\&},1]}-\frac{a\sqrt{x}+bx-c}{a}\},\{y(x)\to \frac{1}{a^2\text{Root}[{\mathrm{\#}\text{1}}^6(16e^{12c_1}+16x^3)-\frac{24{\mathrm{\#}\text{1}}^4{x}^2}{a^4}+\frac{8{\mathrm{\#}\text{1}}^3{x}^{3/2}}{a^6}+\frac{9{\mathrm{\#}\text{1}}^{2}x}{a^8}-\frac{6\mathrm{\#}\text{1}\sqrt{x}}{a^{10}}+\frac{1}{a^{12}}\mathrm{\&},2]}-\frac{a\sqrt{x}+bx-c}{a}\},\{y(x)\to \frac{1}{a^2\text{Root}[{\mathrm{\#}\text{1}}^6(16e^{12c_1}+16x^3)-\frac{24{\mathrm{\#}\text{1}}^4{x}^2}{a^4}+\frac{8{\mathrm{\#}\text{1}}^3{x}^{3/2}}{a^6}+\frac{9{\mathrm{\#}\text{1}}^{2}x}{a^8}-\frac{6\mathrm{\#}\text{1}\sqrt{x}}{a^{10}}+\frac{1}{a^{12}}\mathrm{\&},3]}-\frac{a\sqrt{x}+bx-c}{a}\},\{y(x)\to \frac{1}{a^2\text{Root}[{\mathrm{\#}\text{1}}^6(16e^{12c_1}+16x^3)-\frac{24{\mathrm{\#}\text{1}}^4{x}^2}{a^4}+\frac{8{\mathrm{\#}\text{1}}^3{x}^{3/2}}{a^6}+\frac{9{\mathrm{\#}\text{1}}^{2}x}{a^8}-\frac{6\mathrm{\#}\text{1}\sqrt{x}}{a^{10}}+\frac{1}{a^{12}}\mathrm{\&},4]}-\frac{a\sqrt{x}+bx-c}{a}\},\{y(x)\to \frac{1}{a^2\text{Root}[{\mathrm{\#}\text{1}}^6(16e^{12c_1}+16x^3)-\frac{24{\mathrm{\#}\text{1}}^4{x}^2}{a^4}+\frac{8{\mathrm{\#}\text{1}}^3{x}^{3/2}}{a^6}+\frac{9{\mathrm{\#}\text{1}}^{2}x}{a^8}-\frac{6\mathrm{\#}\text{1}\sqrt{x}}{a^{10}}+\frac{1}{a^{12}}\mathrm{\&},5]}-\frac{a\sqrt{x}+bx-c}{a}\},\{y(x)\to \frac{1}{a^2\text{Root}[{\mathrm{\#}\text{1}}^6(16e^{12c_1}+16x^3)-\frac{24{\mathrm{\#}\text{1}}^4{x}^2}{a^4}+\frac{8{\mathrm{\#}\text{1}}^3{x}^{3/2}}{a^6}+\frac{9{\mathrm{\#}\text{1}}^{2}x}{a^8}-\frac{6\mathrm{\#}\text{1}\sqrt{x}}{a^{10}}+\frac{1}{a^{12}}\mathrm{\&},6]}-\frac{a\sqrt{x}+bx-c}{a}\}\}$$

Maple: cpu = 0.202 (sec), leaf count = 83 $$\{y\left(x\right)=\frac{1}{2a}(3\tanh \left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-729x^3{(\tanh \left(\mathit{\_}\mathit{Z}\right))}^6{a}^6+2187x^3{(\tanh \left(\mathit{\_}\mathit{Z}\right))}^4{a}^6-2187x^3{(\tanh \left(\mathit{\_}\mathit{Z}\right))}^2{a}^6+729a^6{x}^3+64{\left({\mathrm{e}}^{\mathit{\_}\mathit{Z}}\right)}^2\mathit{\_}\mathit{C}\mathit{1})\right)a\sqrt{x}-a\sqrt{x}-2bx+2c)\}$$