15.16.3 problem 3

Internal problem ID [3223]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 25, page 112
Problem number : 3
Date solved : Monday, January 27, 2025 at 07:26:37 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 4 x^{2} y^{\prime \prime }-16 x y^{\prime }+25 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

dsolve(4*x^2*diff(y(x),x$2)-16*x*diff(y(x),x)+25*y(x)=0,y(x), singsol=all)
 

\[ y = \left (c_2 \ln \left (x \right )+c_{1} \right ) x^{{5}/{2}} \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 25

DSolve[4*x^2*D[y[x],{x,2}]-16*x*D[y[x],x]+25*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} x^{5/2} (5 c_2 \log (x)+2 c_1) \]