3.212   ODE No. 212

$$\boxed{{\displaystyle y\left(x\right)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+f({\left(y\left(x\right)\right)}^2+x^2)g\left(x\right)+x=0}}$$

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

Mathematica: cpu = 22.411346 (sec), leaf count = 92 $$\text{Solve}[{\int }_1^{y(x)}(\frac{K[2]}{f(K[2{]}^2+x^2)}-{\int }_1^x-\frac{2K[1]K[2]f^{\prime }(K[1{]}^2+K[2{]}^2)}{f{(K[1{]}^2+K[2{]}^2)}^2}dK[1])dK[2]+{\int }_1^x(\frac{K[1]}{f(K[1{]}^2+y(x{)}^2)}+g(K[1]))dK[1]=c_1,y(x)]$$

Maple: cpu = 0.094 (sec), leaf count = 30 $$\{{\int }_{\mathit{\_}\mathit{b}}^{y\left(x\right)}\frac{\mathit{\_}\mathit{a}}{f({\mathit{\_}\mathit{a}}^2+x^2)}\mathrm{d}\mathit{\_}\mathit{a}+\int g\left(x\right)\mathrm{d}x-\mathit{\_}\mathit{C}\mathit{1}=0\}$$