Internal problem ID [5552]
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(d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 y^{\prime }+5 y-25 x^{2}-12=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 30
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+5*y(x)=25*x^2+12,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{x} \sin \left (2 x \right ) c_{2}+{\mathrm e}^{x} \cos \left (2 x \right ) c_{1}+5 x^{2}+4 x +2 \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 33
DSolve[y''[x]-2*y'[x]+5*y[x]==25*x^2+12,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x (5 x+4)+e^x (c_2 \cos (2 x)+c_1 \sin (2 x))+2 \\ \end{align*}