2.578   ODE No. 578

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

$$y^{\prime }(x)=F(y(x)-x^2)+2x$$ ✓ Mathematica : cpu = 0.161354 (sec), leaf count = 100

$$\text{Solve}[{\int }_1^{y(x)}-\frac{F(K[2]-x^2){\int }_1^x-\frac{2K[1]F^{\prime }(K[2]-K[1{]}^2)}{F{(K[2]-K[1{]}^2)}^2}dK[1]+1}{F(K[2]-x^2)}dK[2]+{\int }_1^x(\frac{2K[1]}{F(y(x)-K[1{]}^2)}+1)dK[1]=c_1,y(x)]$$ ✓ Maple : cpu = 0.12 (sec), leaf count = 22

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