Internal problem ID [13786]
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 (j).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y=\ln \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve(x^2*diff(y(x),x$2)+5*x*diff(y(x),x)+4*y(x)=ln(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (x^{2}+4 c_{1} \right ) \ln \left (x \right )-x^{2}+4 c_{2}}{4 x^{2}} \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 29
DSolve[x^2*y''[x]+5*x*y'[x]+4*y[x]==Log[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_1}{x^2}+\left (\frac {1}{4}+\frac {2 c_2}{x^2}\right ) \log (x)-\frac {1}{4} \]