82.48.12 problem Ex. 12

Internal problem ID [18993]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VIII. End of chapter problems at page 107
Problem number : Ex. 12
Date solved : Tuesday, January 28, 2025 at 12:44:43 PM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} y^{\prime \prime }&=\frac {a}{x} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 18

dsolve(diff(y(x),x$2)=a/x,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 21

DSolve[D[y[x],{x,2}]==a/x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -a x+a x \log (x)+c_2 x+c_1 \]