Internal problem ID [5556]
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 2.2. THE METHOD OF UNDETERMINED
COEFFICIENTS. Page 67
Problem number: 1(h).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 y^{\prime }-12 x +10=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 21
dsolve(diff(y(x),x$2)-2*diff(y(x),x)=12*x-10,y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{2 x} c_{1}}{2}-3 x^{2}+2 x +c_{2} \]
✓ Solution by Mathematica
Time used: 0.076 (sec). Leaf size: 26
DSolve[y''[x]-2*y'[x]==12*x-10,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to (2-3 x) x+\frac {1}{2} c_1 e^{2 x}+c_2 \\ \end{align*}