Internal problem ID [5965]
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]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+5 y=3 \,{\mathrm e}^{-x}+2 x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \sin \left (x \right ) {\mathrm e}^{2 x} c_{2} +\cos \left (x \right ) {\mathrm e}^{2 x} c_{1} +\frac {3 \,{\mathrm e}^{-x}}{10}+\frac {2 x^{2}}{5}+\frac {16 x}{25}+\frac {44}{125} \]
✓ Solution by Mathematica
Time used: 0.316 (sec). Leaf size: 47
DSolve[y''[x]-4*y'[x]+5*y[x]==3*Exp[-x]+2*x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{250} \left (100 x^2+160 x+75 e^{-x}+88\right )+c_2 e^{2 x} \cos (x)+c_1 e^{2 x} \sin (x) \]