Internal problem ID [5515]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Problems for Review and Discovery. Page
53
Problem number: 4(d).
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 }-5 x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 21
dsolve(x*diff(y(x),x$2)-3*diff(y(x),x)=5*x,y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (2 c_{1} x^{2}-5\right )^{2}}{16 c_{1}}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 23
DSolve[x*y''[x]-3*y'[x]==5*x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} x^2 \left (-5+c_1 x^2\right )+c_2 \\ \end{align*}