ODE
\[ 2 \sqrt {a y'(x)}+x y'(x)-y(x)=0 \] ODE Classification
[[_homogeneous, `class G`], _Clairaut]
Book solution method
Clairaut’s equation and related types, main form
Mathematica ✓
cpu = 0.173367 (sec), leaf count = 20
\[\left \{\left \{y(x)\to 2 \sqrt {a c_1}+c_1 x\right \}\right \}\]
Maple ✓
cpu = 0.083 (sec), leaf count = 15
\[\left [y \left (x \right ) = 2 \sqrt {\textit {\_C1} a}+\textit {\_C1} x\right ]\] Mathematica raw input
DSolve[-y[x] + x*y'[x] + 2*Sqrt[a*y'[x]] == 0,y[x],x]
Mathematica raw output
{{y[x] -> x*C[1] + 2*Sqrt[a*C[1]]}}
Maple raw input
dsolve(2*(a*diff(y(x),x))^(1/2)+x*diff(y(x),x)-y(x) = 0, y(x))
Maple raw output
[y(x) = 2*(_C1*a)^(1/2)+_C1*x]