60.3.389 problem 1395

Internal problem ID [11399]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1395
Date solved : Monday, January 27, 2025 at 11:19:21 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} y^{\prime \prime }&=-\frac {y}{\left (a x +b \right )^{4}} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 39

dsolve(diff(diff(y(x),x),x) = -1/(a*x+b)^4*y(x),y(x), singsol=all)
 

\[ y = \left (a x +b \right ) \left (c_{1} \sin \left (\frac {1}{a \left (a x +b \right )}\right )+c_{2} \cos \left (\frac {1}{a \left (a x +b \right )}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.242 (sec). Leaf size: 62

DSolve[D[y[x],{x,2}] == -(y[x]/(b + a*x)^4),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} e^{-1-\frac {i}{a (a x+b)}} (a x+b) \left (2 c_1 e^{\frac {2 i}{a (a x+b)}}-i e^2 c_2\right ) \]