Internal problem ID [13413]
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: 22.10 (k).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+5 y=10 x^{2}+4 x +8} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 30
dsolve(diff(y(x),x$2)-4*diff(y(x),x)+5*y(x)=10*x^2+4*x+8,y(x), singsol=all)
\[ y = {\mathrm e}^{2 x} \sin \left (x \right ) c_{2} +{\mathrm e}^{2 x} \cos \left (x \right ) c_{1} +2 x^{2}+4 x +4 \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 35
DSolve[y''[x]-4*y'[x]+5*y[x]==10*x^2+4*x+8,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 2 x^2+4 x+c_2 e^{2 x} \cos (x)+c_1 e^{2 x} \sin (x)+4 \]