ODE
\[ \left (y(x)^2+1\right ) y''(x)=(a+3 y(x)) y'(x)^2 \] ODE Classification
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✗
cpu = 599.998 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 0.034 (sec), leaf count = 41
\[ \left \{ {\frac {y \left ( x \right ) -a}{{{\rm e}^{a\arctan \left ( y \left ( x \right ) \right ) }} \left ( {a}^{2}+1 \right ) }{\frac {1}{\sqrt {1+ \left ( y \left ( x \right ) \right ) ^{2}}}}}-{\it \_C1}\,x-{\it \_C2}=0 \right \} \] Mathematica raw input
DSolve[(1 + y[x]^2)*y''[x] == (a + 3*y[x])*y'[x]^2,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve((1+y(x)^2)*diff(diff(y(x),x),x) = (a+3*y(x))*diff(y(x),x)^2, y(x),'implicit')
Maple raw output
1/(1+y(x)^2)^(1/2)*(y(x)-a)/exp(a*arctan(y(x)))/(a^2+1)-_C1*x-_C2 = 0