73.17.6 problem 6

Internal problem ID [15540]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 25. Review exercises for part III. page 447
Problem number : 6
Date solved : Tuesday, January 28, 2025 at 08:01:36 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }-7 x y^{\prime }+16 y&=0 \end{align*}

✓ Solution by Maple

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

dsolve(x^2*diff(y(x),x$2)-7*x*diff(y(x),x)+16*y(x)=0,y(x), singsol=all)
 

\[ y = x^{4} \left (\ln \left (x \right ) c_{2} +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 18

DSolve[x^2*D[y[x],{x,2}]-7*x*D[y[x],x]+16*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^4 (4 c_2 \log (x)+c_1) \]