73.16.10 problem 24.1 (j)

Internal problem ID [15522]
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)
Date solved : Tuesday, January 28, 2025 at 08:01:02 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y&=\ln \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (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)
 

\[ y = \frac {\left (x^{2}+4 c_{1} \right ) \ln \left (x \right )-x^{2}+4 c_{2}}{4 x^{2}} \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 29

DSolve[x^2*D[y[x],{x,2}]+5*x*D[y[x],x]+4*y[x]==Log[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_1}{x^2}+\left (\frac {1}{4}+\frac {2 c_2}{x^2}\right ) \log (x)-\frac {1}{4} \]