78.11.9 problem 7 (c)

Internal problem ID [18280]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 16. The Use of a Known Solution to find Another. Problems at page 121
Problem number : 7 (c)
Date solved : Tuesday, January 28, 2025 at 11:45:05 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: 0.003 (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: 0.019 (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]
 

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