ODE
\[ (a+b x)^4 y''(x)+y(x)=0 \] ODE Classification
[[_Emden, _Fowler]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.266459 (sec), leaf count = 57
\[\left \{\left \{y(x)\to \frac {1}{2} e^{-\frac {i}{b (a+b x)}} (a+b x) \left (2 c_1 e^{\frac {2 i}{b (a+b x)}}-i c_2\right )\right \}\right \}\]
Maple ✓
cpu = 0.118 (sec), leaf count = 43
\[\left [y \left (x \right ) = \textit {\_C1} \left (b x +a \right ) \sin \left (\frac {1}{b \left (b x +a \right )}\right )+\textit {\_C2} \left (b x +a \right ) \cos \left (\frac {1}{b \left (b x +a \right )}\right )\right ]\] Mathematica raw input
DSolve[y[x] + (a + b*x)^4*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> ((a + b*x)*(2*E^((2*I)/(b*(a + b*x)))*C[1] - I*C[2]))/(2*E^(I/(b*(a + b*x))))}}
Maple raw input
dsolve((b*x+a)^4*diff(diff(y(x),x),x)+y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*(b*x+a)*sin(1/b/(b*x+a))+_C2*(b*x+a)*cos(1/b/(b*x+a))]