2.951   ODE No. 951

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

$$y^{\prime }(x)=\frac{3}{4}{a}^2{x}^{2}y(x)+\frac{3a^2{x}^4}{16}+\frac{a^3{x}^3}{8}+\frac{a^2{x}^2}{4}+\frac{3}{4}a{x}^{3}y(x)+\frac{3a{x}^5}{32}+\frac{a{x}^3}{4}+\frac{3}{2}axy(x{)}^2+axy(x)+\frac{3}{16}{x}^{4}y(x)+\frac{3}{4}{x}^{2}y(x{)}^2+\frac{1}{2}{x}^{2}y(x)+\frac{x^6}{64}+\frac{x^4}{16}+y(x{)}^3+y(x{)}^2-\frac{x}{2}+1$$ ✓ Mathematica : cpu = 0.395079 (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 = 0.221 (sec), leaf count = 41

$$\{y\left(x\right)=-\frac{x^2}{4}-\frac{ax}{2}+\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-x+2{\int }^{\mathit{\_}\mathit{Z}}{(2{\mathit{\_}\mathit{a}}^3+2{\mathit{\_}\mathit{a}}^2+a+2)}^{-1}d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1})\}$$