73.15.81 problem 22.15 (h)

Internal problem ID [15512]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 22. Method of undetermined coefficients. Additional exercises page 412
Problem number : 22.15 (h)
Date solved : Tuesday, January 28, 2025 at 08:00:38 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y&=64 x^{2} \ln \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 25

dsolve(x^2*diff(y(x),x$2)+5*x*diff(y(x),x)+4*y(x)=64*x^2*ln(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 29

DSolve[x^2*D[y[x],{x,2}]+5*x*D[y[x],x]+4*y[x]==64*x^2*Log[x],y[x],x,IncludeSingularSolutions -> True]
 

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