49.13.4 problem 1(d)

Internal problem ID [7680]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 3. Linear equations with variable coefficients. Page 121
Problem number : 1(d)
Date solved : Monday, January 27, 2025 at 03:09:45 PM
CAS classification : [_Laguerre]

\begin{align*} x y^{\prime \prime }-\left (1+x \right ) y^{\prime }+y&=0 \end{align*}

Using reduction of order method given that one solution is

\begin{align*} y&={\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 13

dsolve([x*diff(y(x),x$2)-(x+1)*diff(y(x),x)+y(x)=0,exp(x)],singsol=all)
 

\[ y = {\mathrm e}^{x} c_{2} +c_{1} x +c_{1} \]

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 19

DSolve[x*D[y[x],{x,2}]-(x+1)*D[y[x],x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 e^x-c_2 (x+1) \]