ODE No. 337

\[ \left (\sqrt {x^2+y(x)^2}+x\right ) y'(x)-y(x)=0 \]

✓ Mathematica : cpu = 0.229011 (sec), leaf count = 52

DSolve[-y[x] + (x + Sqrt[x^2 + y[x]^2])*Derivative[1][y][x] == 0,y[x],x]

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

✓ Maple : cpu = 0.132 (sec), leaf count = 28

dsolve(((y(x)^2+x^2)^(1/2)+x)*diff(y(x),x)-y(x) = 0,y(x))

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