Internal problem ID [13528]
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: 50.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {x^{2} y^{\prime \prime }+3 x y^{\prime }+y=\frac {1}{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(x^2*diff(y(x),x$2)+3*x*diff(y(x),x)+y(x)=1/x,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{2}}{x}+\frac {\ln \left (x \right ) c_{1}}{x}+\frac {\ln \left (x \right )^{2}}{2 x} \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 27
DSolve[x^2*y''[x]+3*x*y'[x]+y[x]==1/x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\log ^2(x)+2 c_2 \log (x)+2 c_1}{2 x} \]