ODE
\[ \sqrt {a^2-4 b-4 c y(x)}+a+2 x y'(x)+4 y(x)=0 \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.587345 (sec), leaf count = 112
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\frac {1}{4} \left (\frac {2 c \tanh ^{-1}\left (\frac {c-2 \sqrt {a^2-4 (\text {$\#$1} c+b)}}{\sqrt {4 a^2+4 a c-16 b+c^2}}\right )}{\sqrt {4 a^2+4 a c-16 b+c^2}}+\log \left (-c \left (\sqrt {a^2-4 (\text {$\#$1} c+b)}+4 \text {$\#$1}+a\right )\right )\right )\& \right ]\left [-\frac {\log (x)}{2}+c_1\right ]\right \}\right \}\]
Maple ✓
cpu = 0.033 (sec), leaf count = 38
\[\left [\ln \left (x \right )+\int _{}^{y \left (x \right )}-\frac {1}{-2 \textit {\_a} -\frac {a}{2}-\frac {\sqrt {-4 \textit {\_a} c +a^{2}-4 b}}{2}}d \textit {\_a} +\textit {\_C1} = 0\right ]\] Mathematica raw input
DSolve[a + 4*y[x] + Sqrt[a^2 - 4*b - 4*c*y[x]] + 2*x*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> InverseFunction[((2*c*ArcTanh[(c - 2*Sqrt[a^2 - 4*(b + c*#1)])/Sqrt[4*a^2 - 16*b + 4*a*c + c^2]])/Sqrt[4*a^2 - 16*b + 4*a*c + c^2] + Log[-(c*(a + 4*#1 + Sqrt[a^2 - 4*(b + c*#1)]))])/4 & ][C[1] - Log[x]/2]}}
Maple raw input
dsolve(2*x*diff(y(x),x)+4*y(x)+a+(a^2-4*b-4*c*y(x))^(1/2) = 0, y(x))
Maple raw output
[ln(x)+Intat(-1/(-2*_a-1/2*a-1/2*(-4*_a*c+a^2-4*b)^(1/2)),_a = y(x))+_C1 = 0]