83.28.5 problem 5

Internal problem ID [19370]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (B) at page 106
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 01:35:38 PM
CAS classification : [[_2nd_order, _quadrature]]

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

✓ Solution by Maple

Time used: 0.000 (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]
 

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