Internal problem ID [5586]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }+3 y^{\prime }=0} \end {gather*} Given that one solution of the ode is \begin {align*} y_1 &= 1 \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 11
dsolve([x*diff(y(x),x$2)+3*diff(y(x),x)=0,1],y(x), singsol=all)
\[ y \relax (x ) = c_{1}+\frac {c_{2}}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 17
DSolve[x*y''[x]+3*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2-\frac {c_1}{2 x^2} \\ \end{align*}