8.9.16 problem 52

Internal problem ID [860]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.3, second order linear equations. Page 323
Problem number : 52
Date solved : Wednesday, February 05, 2025 at 04:34:37 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 19

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

\[ y = c_1 \sin \left (3 \ln \left (x \right )\right )+c_2 \cos \left (3 \ln \left (x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 22

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

\[ y(x)\to c_1 \cos (3 \log (x))+c_2 \sin (3 \log (x)) \]