3.841   ODE No. 841

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=\frac{b{x}^3+c^2\sqrt{a}-2cb{x}^2\sqrt{a}+2c{\left(y\left(x\right)\right)}^2{a}^{3/2}+b^2{x}^4\sqrt{a}-2{\left(y\left(x\right)\right)}^2{a}^{3/2}b{x}^2+a^{5/2}{\left(y\left(x\right)\right)}^4}{a{x}^{2}y\left(x\right)}=0}}$$

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

Mathematica: cpu = 1.255659 (sec), leaf count = 236 $$\{\{y(x)\to -\frac{\sqrt{2a^{5/2}b{x}^2-2a^{5/2}c+4a^3{b}^2{x}^3-4a^{3}bcx+a^{2}x+4\sqrt{a}{b}^2{c}_1{x}^2-4\sqrt{a}bc{c}_1+2b{c}_{1}x}}{\sqrt{2}\sqrt{2a^{3/2}b{c}_1+a^{7/2}+2a^{4}bx}}\},\{y(x)\to \frac{\sqrt{2a^{5/2}b{x}^2-2a^{5/2}c+4a^3{b}^2{x}^3-4a^{3}bcx+a^{2}x+4\sqrt{a}{b}^2{c}_1{x}^2-4\sqrt{a}bc{c}_1+2b{c}_{1}x}}{\sqrt{2}\sqrt{2a^{3/2}b{c}_1+a^{7/2}+2a^{4}bx}}\}\}$$

Maple: cpu = 0.234 (sec), leaf count = 97 $$\{y\left(x\right)=\frac{1}{x\mathit{\_}\mathit{C}\mathit{1}+1}\sqrt{((x\mathit{\_}\mathit{C}\mathit{1}+1)(b{x}^2-c)\sqrt{a}+\frac{x}{2})(x\mathit{\_}\mathit{C}\mathit{1}+1)a^{\frac{3}{2}}}{a}^{-\frac{3}{2}},y\left(x\right)=-2\frac{\sqrt{((x\mathit{\_}\mathit{C}\mathit{1}+1)(b{x}^2-c)\sqrt{a}+x/2)(x\mathit{\_}\mathit{C}\mathit{1}+1)a^{3/2}}}{a^{3/2}(2x\mathit{\_}\mathit{C}\mathit{1}+2)}\}$$