2.879   ODE No. 879

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

✓ Mathematica : cpu = 0.188899 (sec), leaf count = 128

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

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

✓ Maple : cpu = 0.388 (sec), leaf count = 55

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

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