50.12.3 problem 2

Internal problem ID [8007]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Second-Order Linear Equations. Section 2.4. THE USE OF A KNOWN SOLUTION TO FIND ANOTHER. Page 74
Problem number : 2
Date solved : Monday, January 27, 2025 at 03:36:44 PM
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: 0.002 (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: 0.011 (sec). Leaf size: 17

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

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