2.684   ODE No. 684

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

✓ Mathematica : cpu = 0.0961161 (sec), leaf count = 86

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

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

✓ Maple : cpu = 3.719 (sec), leaf count = 30

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

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