ODE No. 684

\[ y'(x)=\frac {x^2 \sqrt {x^2+y(x)^2}+y(x)}{x} \] Mathematica : cpu = 0.123257 (sec), leaf count = 20

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

\[\left \{\left \{y(x)\to x \sinh \left (\frac {1}{2} \left (x^2+2 c_1\right )\right )\right \}\right \}\] Maple : cpu = 3.691 (sec), leaf count = 30

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

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