Internal problem ID [14730]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number: 21.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y=\frac {1}{x^{5}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve(x^2*diff(y(x),x$2)+5*x*diff(y(x),x)+4*y(x)=1/x^5,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{2}}{x^{2}}+\frac {\ln \left (x \right ) c_{1}}{x^{2}}+\frac {1}{9 x^{5}} \]
✓ Solution by Mathematica
Time used: 0.105 (sec). Leaf size: 28
DSolve[x^2*y''[x]+5*x*y'[x]+4*y[x]==1/x^5,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{9 x^5}+\frac {c_1}{x^2}+\frac {2 c_2 \log (x)}{x^2} \]