73.17.38 problem 38

Internal problem ID [15572]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 25. Review exercises for part III. page 447
Problem number : 38
Date solved : Tuesday, January 28, 2025 at 08:02:27 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y&=18 \ln \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 20

dsolve(x^2*diff(y(x),x$2)+2*x*diff(y(x),x)-6*y(x)=18*ln(x),y(x), singsol=all)
 

\[ y = \frac {c_{2}}{x^{3}}+c_{1} x^{2}-\frac {1}{2}-3 \ln \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 25

DSolve[x^2*D[y[x],{x,2}]+2*x*D[y[x],x]-6*y[x]==18*Log[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_1}{x^3}+c_2 x^2-3 \log (x)-\frac {1}{2} \]