Internal problem ID [13516]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y=18 \ln \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \frac {c_{2}}{x^{3}}+c_{1} x^{2}-3 \ln \left (x \right )-\frac {1}{2} \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 25
DSolve[x^2*y''[x]+2*x*y'[x]-6*y[x]==18*Log[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_1}{x^3}+c_2 x^2-3 \log (x)-\frac {1}{2} \]