Internal problem ID [5490]
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. Section 1.9. Reduction of Order. Page
38
Problem number: 1(g).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {y^{\prime }+x y^{\prime \prime }-4 x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
dsolve(x*diff(y(x),x$2)+diff(y(x),x)=4*x,y(x), singsol=all)
\[ y \relax (x ) = x^{2}+c_{1} \ln \relax (x )+c_{2} \]
✓ Solution by Mathematica
Time used: 0.042 (sec). Leaf size: 16
DSolve[x*y''[x]+y'[x]==4*x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^2+c_1 \log (x)+c_2 \\ \end{align*}