78.11.3 problem 3

Internal problem ID [18274]
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 : 3
Date solved : Tuesday, January 28, 2025 at 11:45:01 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x y^{\prime \prime }+3 y^{\prime }&=0 \end{align*}

Using reduction of order method given that one solution is

\begin{align*} y&=1 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 11

dsolve([x*diff(y(x),x$2)+3*diff(y(x),x)=0,1],singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 17

DSolve[x*D[y[x],{x,2}] +3*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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