7.9.18 problem 40

Internal problem ID [266]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.2 (General solutions of linear equations). Problems at page 122
Problem number : 40
Date solved : Monday, January 27, 2025 at 02:43:08 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*}

Using reduction of order method given that one solution is

\begin{align*} y&=x \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 12

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

\[ y = x \left (c_1 +c_2 \,{\mathrm e}^{x}\right ) \]

✓ Solution by Mathematica

Time used: 0.022 (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]
 

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