3.951   ODE No. 951

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=-x/2+1+{\left(y\left(x\right)\right)}^2+1/2x^{2}y\left(x\right)+axy\left(x\right)+1/16x^4+1/4a{x}^3+1/4a^2{x}^2+{\left(y\left(x\right)\right)}^3+3/4x^2{\left(y\left(x\right)\right)}^2+3/2ax{\left(y\left(x\right)\right)}^2+3/16y\left(x\right)x^4+3/4y\left(x\right)a{x}^3+3/4a^2{x}^{2}y\left(x\right)+\frac{x^6}{64}+\frac{3x^{5}a}{32}+3/16a^2{x}^4+1/8a^3{x}^3=0}}$$

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

Mathematica: cpu = 0.144018 (sec), leaf count = 140 $$\text{Solve}[-\frac{1}{3}(27a+58{)}^{2/3}\text{RootSum}[{\mathrm{\#}\text{1}}^3(27a+58{)}^{2/3}-32^{2/3}\mathrm{\#}\text{1}+(27a+58{)}^{2/3}\mathrm{\&},\frac{\log (\frac{\sqrt[3]{2}(\frac{1}{4}(6ax+3x^2+4)+3y(x))}{\sqrt[3]{27a+58}}-\mathrm{\#}\text{1})}{2^{2/3}-{\mathrm{\#}\text{1}}^2(27a+58{)}^{2/3}}\mathrm{\&}]=\frac{(27a+58{)}^{2/3}x}{92^{2/3}}+c_1,y(x)]$$

Maple: cpu = 0.062 (sec), leaf count = 41 $$\{y\left(x\right)=-\frac{x^2}{4}-\frac{ax}{2}+\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-x+2{\int }^{\mathit{\_}\mathit{Z}}{(2{\mathit{\_}\mathit{a}}^3+2{\mathit{\_}\mathit{a}}^2+a+2)}^{-1}d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1})\}$$