35.7.12 problem 16 (c)

Internal problem ID [6194]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 7. Other second-Order equations. page 435
Problem number : 16 (c)
Date solved : Monday, January 27, 2025 at 01:47:20 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }+7 x y^{\prime }+9 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 14

dsolve(x^2*diff(y(x),x$2)+7*x*diff(y(x),x)+9*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{2} \ln \left (x \right )+c_{1}}{x^{3}} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 18

DSolve[x^2*D[y[x],{x,2}]+7*x*D[y[x],x]+9*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {3 c_2 \log (x)+c_1}{x^3} \]