2.692   ODE No. 692

\[ y'(x)=\frac {x^3 \sqrt {x^2+y(x)^2}+y(x)}{x} \]

✓ Mathematica : cpu = 0.106517 (sec), leaf count = 86

DSolve[Derivative[1][y][x] == (y[x] + x^3*Sqrt[x^2 + y[x]^2])/x,y[x],x]
 

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

✓ Maple : cpu = 3.726 (sec), leaf count = 30

dsolve(diff(y(x),x) = (y(x)+x^3*(y(x)^2+x^2)^(1/2))/x,y(x))
 

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