2.922   ODE No. 922

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

$$y^{\prime }(x)=\frac{y(x{)}^2}{-3x^{2}y(x)+x^2\sqrt{y(x)}+x^3+3xy(x{)}^2-2xy(x{)}^{3/2}-y(x{)}^3+y(x{)}^{5/2}+y(x{)}^2+y(x{)}^{3/2}}$$ ✓ Mathematica : cpu = 1.1555 (sec), leaf count = 882

$$\text{Solve}[{\int }_1^{y(x)}(\frac{-x-K[1]}{2(-2x^3+6K[1]x^2-2\sqrt{K[1]}{x}^2-6K[1{]}^{2}x+4K[1{]}^{3/2}x+K[1]x+2K[1{]}^3-2K[1{]}^{5/2}-K[1{]}^2-2K[1{]}^{3/2})}+\text{RootSum}[2K[1{]}^3-2K[1{]}^{5/2}-6\mathrm{\#}\text{1}K[1{]}^2-K[1{]}^2+4\mathrm{\#}\text{1}K[1{]}^{3/2}-2K[1{]}^{3/2}+6{\mathrm{\#}\text{1}}^{2}K[1]+\mathrm{\#}\text{1}K[1]-2{\mathrm{\#}\text{1}}^2\sqrt{K[1]}-2{\mathrm{\#}\text{1}}^3\mathrm{\&},\frac{\log (x-\mathrm{\#}\text{1})}{6K[1{]}^2-4K[1{]}^{3/2}-12\mathrm{\#}\text{1}K[1]-K[1]+4\mathrm{\#}\text{1}\sqrt{K[1]}+6{\mathrm{\#}\text{1}}^2}\mathrm{\&}]+\frac{\text{RootSum}[2K[1{]}^3-2K[1{]}^{5/2}-6\mathrm{\#}\text{1}K[1{]}^2-K[1{]}^2+4\mathrm{\#}\text{1}K[1{]}^{3/2}-2K[1{]}^{3/2}+6{\mathrm{\#}\text{1}}^{2}K[1]+\mathrm{\#}\text{1}K[1]-2{\mathrm{\#}\text{1}}^2\sqrt{K[1]}-2{\mathrm{\#}\text{1}}^3\mathrm{\&},\frac{10\log (x-\mathrm{\#}\text{1})K[1{]}^3-10K[1{]}^3-10\log (x-\mathrm{\#}\text{1})K[1{]}^{5/2}-14K[1{]}^{5/2}-10x\log (x-\mathrm{\#}\text{1})K[1{]}^2-5\log (x-\mathrm{\#}\text{1})K[1{]}^2-20\log (x-\mathrm{\#}\text{1})\mathrm{\#}\text{1}K[1{]}^2+20\mathrm{\#}\text{1}K[1{]}^2+8K[1{]}^2-38x\log (x-\mathrm{\#}\text{1})K[1{]}^{3/2}-10\log (x-\mathrm{\#}\text{1})K[1{]}^{3/2}+58\log (x-\mathrm{\#}\text{1})\mathrm{\#}\text{1}K[1{]}^{3/2}-10\mathrm{\#}\text{1}K[1{]}^{3/2}+5K[1{]}^{3/2}+10\log (x-\mathrm{\#}\text{1}){\mathrm{\#}\text{1}}^{2}K[1]-10{\mathrm{\#}\text{1}}^{2}K[1]+11x\log (x-\mathrm{\#}\text{1})K[1]+20x\log (x-\mathrm{\#}\text{1})\mathrm{\#}\text{1}K[1]-6\log (x-\mathrm{\#}\text{1})\mathrm{\#}\text{1}K[1]+3\mathrm{\#}\text{1}K[1]-48\log (x-\mathrm{\#}\text{1}){\mathrm{\#}\text{1}}^2\sqrt{K[1]}+24{\mathrm{\#}\text{1}}^2\sqrt{K[1]}+38x\log (x-\mathrm{\#}\text{1})\mathrm{\#}\text{1}\sqrt{K[1]}-10x\log (x-\mathrm{\#}\text{1}){\mathrm{\#}\text{1}}^2}{-50K[1{]}^3+50K[1{]}^{5/2}+50xK[1{]}^2+100\mathrm{\#}\text{1}K[1{]}^2+25K[1{]}^2+190xK[1{]}^{3/2}-290\mathrm{\#}\text{1}K[1{]}^{3/2}+50K[1{]}^{3/2}-50{\mathrm{\#}\text{1}}^{2}K[1]+259xK[1]-100x\mathrm{\#}\text{1}K[1]-284\mathrm{\#}\text{1}K[1]+240{\mathrm{\#}\text{1}}^2\sqrt{K[1]}-190x\mathrm{\#}\text{1}\sqrt{K[1]}+50x{\mathrm{\#}\text{1}}^2}\mathrm{\&}]}{K[1]}+\frac{1}{2K[1]})dK[1]-\text{RootSum}[-2{\mathrm{\#}\text{1}}^3+6y(x){\mathrm{\#}\text{1}}^2-2\sqrt{y(x)}{\mathrm{\#}\text{1}}^2-6y(x{)}^2\mathrm{\#}\text{1}+4y(x{)}^{3/2}\mathrm{\#}\text{1}+y(x)\mathrm{\#}\text{1}+2y(x{)}^3-2y(x{)}^{5/2}-y(x{)}^2-2y(x{)}^{3/2}\mathrm{\&},\frac{\log (x-\mathrm{\#}\text{1})}{6{\mathrm{\#}\text{1}}^2-12y(x)\mathrm{\#}\text{1}+4\sqrt{y(x)}\mathrm{\#}\text{1}+6y(x{)}^2-4y(x{)}^{3/2}-y(x)}\mathrm{\&}]y(x)=c_1,y(x)]$$ ✓ Maple : cpu = 0.351 (sec), leaf count = 47

$$\{\frac{\ln \left(y\left(x\right)\right)}{2}-{\int }^{x\frac{1}{\sqrt{y\left(x\right)}}-\sqrt{y\left(x\right)}}{(2{\mathit{\_}\mathit{a}}^3+2{\mathit{\_}\mathit{a}}^2-\mathit{\_}\mathit{a}+2)}^{-1}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0\}$$