Internal problem ID [13467]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {x^{2} y^{\prime \prime }-2 y=\frac {1}{x -2}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 50
dsolve(x^2*diff(y(x),x$2)-2*y(x)=1/(x-2),y(x), singsol=all)
\[ y = \frac {c_{1}}{x}+c_{2} x^{2}-\frac {\ln \left (x \right ) x^{3}-\ln \left (x -2\right ) x^{3}-2 x^{2}+8 \ln \left (x -2\right )-2 x}{24 x} \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 57
DSolve[x^2*y''[x]-2*y[x]==1/(x-2),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^3 \log (2-x)-x^3 \log (x)+24 c_2 x^3+2 x^2+2 x-8 \log (6-3 x)+24 c_1}{24 x} \]