Internal problem ID [8974]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1395.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\frac {y}{\left (a x +b \right )^{4}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 43
dsolve(diff(diff(y(x),x),x) = -1/(a*x+b)^4*y(x),y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (a x +b \right ) \sin \left (\frac {1}{a \left (a x +b \right )}\right )+c_{2} \left (a x +b \right ) \cos \left (\frac {1}{a \left (a x +b \right )}\right ) \]
✓ Solution by Mathematica
Time used: 0.06 (sec). Leaf size: 57
DSolve[y''[x] == -(y[x]/(b + a*x)^4),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} e^{-\frac {i}{a (a x+b)}} (a x+b) \left (2 c_1 e^{\frac {2 i}{a (a x+b)}}-i c_2\right ) \\ \end{align*}