2.841   ODE No. 841

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

$$y^{\prime }(x)=\frac{-2a^{3/2}b{x}^{2}y(x{)}^2+2a^{3/2}cy(x{)}^2+a^{5/2}y(x{)}^4+\sqrt{a}{b}^2{x}^4-2\sqrt{a}bc{x}^2+\sqrt{a}{c}^2+b{x}^3}{a{x}^{2}y(x)}$$ ✓ Mathematica : cpu = 1.36392 (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 = 0.319 (sec), leaf count = 97

$$\{y\left(x\right)=\frac{1}{\mathit{\_}\mathit{C}\mathit{1}x+1}\sqrt{a^{\frac{3}{2}}(\mathit{\_}\mathit{C}\mathit{1}x+1)((\mathit{\_}\mathit{C}\mathit{1}x+1)(b{x}^2-c)\sqrt{a}+\frac{x}{2})}{a}^{-\frac{3}{2}},y\left(x\right)=-2\frac{\sqrt{a^{3/2}(\mathit{\_}\mathit{C}\mathit{1}x+1)((\mathit{\_}\mathit{C}\mathit{1}x+1)(b{x}^2-c)\sqrt{a}+x/2)}}{a^{3/2}(2\mathit{\_}\mathit{C}\mathit{1}x+2)}\}$$