74.15.24 problem 24

Internal problem ID [16463]
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
Date solved : Tuesday, January 28, 2025 at 09:08:30 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+4 y&=\frac {1}{x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.005 (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)
 

\[ y = \sin \left (2 \ln \left (x \right )\right ) c_{2} +\cos \left (2 \ln \left (x \right )\right ) c_{1} +\frac {1}{8 x^{2}} \]

✓ Solution by Mathematica

Time used: 0.114 (sec). Leaf size: 76

DSolve[x^2*D[y[x],{x,2}]+x*D[y[x],x]+4*y[x]==1/x^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \cos (2 \log (x)) \int _1^x-\frac {\sin (2 \log (K[1]))}{2 K[1]^3}dK[1]+\sin (2 \log (x)) \int _1^x\frac {\cos (2 \log (K[2]))}{2 K[2]^3}dK[2]+c_1 \cos (2 \log (x))+c_2 \sin (2 \log (x)) \]