3.950   ODE No. 950

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

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

Mathematica: cpu = 0.167521 (sec), leaf count = 141 $$\text{Solve}[-\frac{1}{3}(27b+58{)}^{2/3}\text{RootSum}[{\mathrm{\#}\text{1}}^3(27b+58{)}^{2/3}-32^{2/3}\mathrm{\#}\text{1}+(27b+58{)}^{2/3}\mathrm{\&},\frac{\log (\frac{\sqrt[3]{2}(\frac{1}{4}(3a{x}^2+6bx+4)+3y(x))}{\sqrt[3]{27b+58}}-\mathrm{\#}\text{1})}{2^{2/3}-{\mathrm{\#}\text{1}}^2(27b+58{)}^{2/3}}\mathrm{\&}]=\frac{(27b+58{)}^{2/3}x}{92^{2/3}}+c_1,y(x)]$$

Maple: cpu = 0.078 (sec), leaf count = 42 $$\{y\left(x\right)=-\frac{a{x}^2}{4}-\frac{bx}{2}+\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-x+2{\int }^{\mathit{\_}\mathit{Z}}{(2{\mathit{\_}\mathit{a}}^3+2{\mathit{\_}\mathit{a}}^2+b+2)}^{-1}d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1})\}$$