Internal problem ID [14733]
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: 24.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+y^{\prime } x +4 y=\frac {1}{x^{2}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)+4*y(x)=1/x^2,y(x), singsol=all)
\[ y \left (x \right ) = c_{2} \sin \left (2 \ln \left (x \right )\right )+\cos \left (2 \ln \left (x \right )\right ) c_{1} +\frac {1}{8 x^{2}} \]
✓ Solution by Mathematica
Time used: 0.053 (sec). Leaf size: 29
DSolve[x^2*y''[x]+x*y'[x]+4*y[x]==1/x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{8 x^2}+c_1 \cos (2 \log (x))+c_2 \sin (2 \log (x)) \]