81.2.7 problem 7

Internal problem ID [18615]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter II. Change of variable. Exercises at page 20
Problem number : 7
Date solved : Tuesday, January 28, 2025 at 12:04:16 PM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 18

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

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