83.30.4 problem 4

Internal problem ID [19383]
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 (D) at page 109
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 01:36:27 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 10

dsolve(diff(y(x),x$2)+1/x*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 13

DSolve[D[y[x],{x,2}]+1/x*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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