Internal problem ID [13456]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y=64 \ln \left (x \right ) x^{2}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 28
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)
\[ y = \frac {c_{2}}{x^{2}}+\frac {\ln \left (x \right ) c_{1}}{x^{2}}+2 x^{2} \left (2 \ln \left (x \right )-1\right ) \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 29
DSolve[x^2*y''[x]+5*x*y'[x]+4*y[x]==64*x^2*Log[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {-2 x^4+2 \left (2 x^4+c_2\right ) \log (x)+c_1}{x^2} \]