2.780   ODE No. 780

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

✓ Mathematica : cpu = 0.119454 (sec), leaf count = 66

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

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

✓ Maple : cpu = 0.917 (sec), leaf count = 27

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

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