2.805   ODE No. 805

\[ y'(x)=\frac {x^4 \sqrt {x^2+y(x)^2}+x y(x)+y(x)}{x (x+1)} \]

✓ Mathematica : cpu = 0.139689 (sec), leaf count = 154

DSolve[Derivative[1][y][x] == (y[x] + x*y[x] + x^4*Sqrt[x^2 + y[x]^2])/(x*(1 + x)),y[x],x]
 

\[\left \{\left \{y(x)\to -\frac {x \tanh \left (\frac {1}{6} \left (2 x^3-3 x^2+6 x-6 \log (x+1)+11+6 c_1\right )\right )}{\sqrt {1-\tanh ^2\left (\frac {1}{6} \left (2 x^3-3 x^2+6 x-6 \log (x+1)+11+6 c_1\right )\right )}}\right \},\left \{y(x)\to \frac {x \tanh \left (\frac {1}{6} \left (2 x^3-3 x^2+6 x-6 \log (x+1)+11+6 c_1\right )\right )}{\sqrt {1-\tanh ^2\left (\frac {1}{6} \left (2 x^3-3 x^2+6 x-6 \log (x+1)+11+6 c_1\right )\right )}}\right \}\right \}\]

✓ Maple : cpu = 1.229 (sec), leaf count = 42

dsolve(diff(y(x),x) = (x*y(x)+y(x)+x^4*(y(x)^2+x^2)^(1/2))/x/(1+x),y(x))
 

\[\ln \left (y \left (x \right )+\sqrt {y \left (x \right )^{2}+x^{2}}\right )-\frac {x^{3}}{3}+\frac {x^{2}}{2}-x +\ln \left (1+x \right )-\ln \left (x \right )-c_{1} = 0\]