7.9.19 problem 41

Internal problem ID [267]
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 : 41
Date solved : Monday, January 27, 2025 at 02:43:08 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (1+x \right ) y^{\prime \prime }-\left (x +2\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: 0.004 (sec). Leaf size: 14

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

\[ y = c_1 \left (x +2\right )+c_2 \,{\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.142 (sec). Leaf size: 29

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

\[ y(x)\to \frac {c_1 e^{x+1}-2 c_2 (x+2)}{\sqrt {2 e}} \]