ODE
\[ x y'(x)=\sqrt {x^2+y(x)^2}+y(x) \] ODE Classification
[[_homogeneous, `class A`], _rational, _dAlembert]
Book solution method
Homogeneous equation
Mathematica ✓
cpu = 0.248376 (sec), leaf count = 13
\[\{\{y(x)\to x \sinh (\log (x)+c_1)\}\}\]
Maple ✓
cpu = 0.047 (sec), leaf count = 27
\[\left [\frac {y \left (x \right )}{x^{2}}+\frac {\sqrt {x^{2}+y \left (x \right )^{2}}}{x^{2}}-\textit {\_C1} = 0\right ]\] Mathematica raw input
DSolve[x*y'[x] == y[x] + Sqrt[x^2 + y[x]^2],y[x],x]
Mathematica raw output
{{y[x] -> x*Sinh[C[1] + Log[x]]}}
Maple raw input
dsolve(x*diff(y(x),x) = y(x)+(x^2+y(x)^2)^(1/2), y(x))
Maple raw output
[1/x^2*y(x)+1/x^2*(x^2+y(x)^2)^(1/2)-_C1 = 0]