40.14.3 problem 24

Internal problem ID [6774]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 19. Linear equations with variable coefficients (Misc. types). Supplemetary problems. Page 132
Problem number : 24
Date solved : Monday, January 27, 2025 at 02:30:14 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x y^{\prime \prime }-y^{\prime }&=-\frac {2}{x}-\ln \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 18

dsolve(x*diff(y(x),x$2)-diff(y(x),x)=-2/x-ln(x),y(x), singsol=all)
 

\[ y = \frac {c_1 \,x^{2}}{2}+\ln \left (x \right ) x +\ln \left (x \right )+c_2 \]

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 23

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

\[ y(x)\to \frac {c_1 x^2}{2}+(x+1) \log (x)+c_2 \]