76.12.13 problem 24

Internal problem ID [17569]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.2 (Theory of second order linear homogeneous equations). Problems at page 226
Problem number : 24
Date solved : Tuesday, January 28, 2025 at 10:44:14 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 12

dsolve(x^2*diff(y(x),x$2)-x*(x+2)*diff(y(x),x)+(x+2)*y(x)=0,y(x), singsol=all)
 

\[ y = x \left (c_{1} +{\mathrm e}^{x} c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 16

DSolve[x^2*D[y[x],{x,2}]-x*(x+2)*D[y[x],x]+(x+2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x \left (c_2 e^x+c_1\right ) \]