73.16.11 problem 24.1 (k)

Internal problem ID [15523]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 24. Variation of parameters. Additional exercises page 444
Problem number : 24.1 (k)
Date solved : Tuesday, January 28, 2025 at 08:01:04 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }-2 y&=\frac {1}{x -2} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 44

dsolve(x^2*diff(y(x),x$2)-2*y(x)=1/(x-2),y(x), singsol=all)
 

\[ y = \frac {\left (x^{3}-8\right ) \ln \left (x -2\right )+24 c_{2} x^{3}-x^{3} \ln \left (x \right )+2 x^{2}+2 x +24 c_{1}}{24 x} \]

✓ Solution by Mathematica

Time used: 0.043 (sec). Leaf size: 56

DSolve[x^2*D[y[x],{x,2}]-2*y[x]==1/(x-2),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^2 \int _1^x\frac {1}{3 (K[1]-2) K[1]^3}dK[1]-\frac {\log (6-3 x)-3 \left (c_2 x^3+c_1\right )}{3 x} \]