2.365   ODE No. 365

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

$$(y(x)f(x^2+y(x{)}^2)-x)y^{\prime }(x)+xf(x^2+y(x{)}^2)+y(x)=0$$ ✓ Mathematica : cpu = 0.349053 (sec), leaf count = 156

$$\text{Solve}[{\int }_1^{y(x)}(\frac{x-f(x^2+K[2{]}^2)K[2]}{x^2+K[2{]}^2}-{\int }_1^x(\frac{-2K[1]K[2]f^{\prime }(K[1{]}^2+K[2{]}^2)-1}{K[1{]}^2+K[2{]}^2}-\frac{2(-f(K[1{]}^2+K[2{]}^2)K[1]-K[2])K[2]}{{(K[1{]}^2+K[2{]}^2)}^2})dK[1])dK[2]+{\int }_1^x\frac{-f(K[1{]}^2+y(x{)}^2)K[1]-y(x)}{K[1{]}^2+y(x{)}^2}dK[1]=c_1,y(x)]$$ ✓ Maple : cpu = 0.289 (sec), leaf count = 42

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