Internal problem ID [6305]
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]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+5 y=25 x^{2}+12} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = {\mathrm e}^{x} \sin \left (2 x \right ) c_{2} +{\mathrm e}^{x} \cos \left (2 x \right ) c_{1} +5 x^{2}+4 x +2 \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 35
DSolve[y''[x]-2*y'[x]+5*y[x]==25*x^2+12,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 5 x^2+4 x+c_2 e^x \cos (2 x)+c_1 e^x \sin (2 x)+2 \]