74.15.27 problem 27

Internal problem ID [16466]
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 : 27
Date solved : Tuesday, January 28, 2025 at 09:08:38 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+4 y&=8 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 20

dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)+4*y(x)=8,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 23

DSolve[x^2*D[y[x],{x,2}]+x*D[y[x],x]+4*y[x]==8,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \cos (2 \log (x))+c_2 \sin (2 \log (x))+2 \]