Internal problem ID [13776]
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]]
\[ \boxed {x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y=64 x^{2} \ln \left (x \right )} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = \frac {\left (4 x^{4}+c_{1} \right ) \ln \left (x \right )-2 x^{4}+c_{2}}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.026 (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]
\[ y(x)\to \frac {-2 x^4+2 \left (2 x^4+c_2\right ) \log (x)+c_1}{x^2} \]