3.366   ODE No. 366

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

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

Mathematica: cpu = 264.973147 (sec), leaf count = 88 $$\text{Solve}[{\int }_1^{y(x)}(-{\int }_1^x(1-2aK[1]K[2]f^{\prime }(aK[2{]}^2+K[1{]}^2))dK[1]-aK[2]f(aK[2{]}^2+x^2)+x)dK[2]+{\int }_1^x(y(x)-K[1]f(K[1{]}^2+ay(x{)}^2))dK[1]=c_1,y(x)]$$

Maple: cpu = 0.046 (sec), leaf count = 45 $$\{-ax{\left(y\left(x\right)\right)}^2\frac{1}{\sqrt{a^2{\left(y\left(x\right)\right)}^2}}-{\int }^{-\frac{a{\left(y\left(x\right)\right)}^2}{2}-\frac{x^2}{2}}f(-2\mathit{\_}\mathit{a})d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}=0\}$$