Internal problem ID [5212]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 2. Linear equations with constant coefficients. Page 69
Problem number: 1(e).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-4 y^{\prime }+5 y-3 \,{\mathrm e}^{-x}-2 x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 36
dsolve(diff(y(x),x$2)-4*diff(y(x),x)+5*y(x)=3*exp(-x)+2*x^2,y(x), singsol=all)
\[ y \relax (x ) = \sin \relax (x ) {\mathrm e}^{2 x} c_{2}+\cos \relax (x ) {\mathrm e}^{2 x} c_{1}+\frac {3 \,{\mathrm e}^{-x}}{10}+\frac {2 x^{2}}{5}+\frac {16 x}{25}+\frac {44}{125} \]
✓ Solution by Mathematica
Time used: 0.144 (sec). Leaf size: 46
DSolve[y''[x]-4*y'[x]+5*y[x]==3*Exp[-x]+2*x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2}{125} (5 x (5 x+8)+22)+\frac {3 e^{-x}}{10}+e^{2 x} (c_2 \cos (x)+c_1 \sin (x)) \\ \end{align*}