Internal problem ID [13708]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 22. Method of undetermined coefficients. Additional exercises page
412
Problem number: 22.5 (c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-6 y^{\prime }+9 y=18 x^{2}+3 x +4} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(diff(y(x),x$2)-6*diff(y(x),x)+9*y(x)=18*x^2+3*x+4,y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{1} x +c_{2} \right ) {\mathrm e}^{3 x}+2 x^{2}+3 x +2 \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 32
DSolve[y''[x]-6*y'[x]+9*y[x]==18*x^2+3*x+4,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 2 x^2+x \left (3+c_2 e^{3 x}\right )+c_1 e^{3 x}+2 \]