9.1.3 problem problem 40

Internal problem ID [930]
Book : Differential equations and linear algebra, 4th ed., Edwards and Penney
Section : Section 5.2, Higher-Order Linear Differential Equations. General solutions of Linear Equations. Page 288
Problem number : problem 40
Date solved : Monday, January 27, 2025 at 03:22:35 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: 0.004 (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: 0.020 (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]
 

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