Internal problem ID [2746]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth
edition, 2015
Section: Chapter 8, Linear differential equations of order n. Section 8.3, The Method of
Undetermined Coefficients. page 525
Problem number: Problem 26.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }+4 y=5 x \,{\mathrm e}^{-2 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(diff(y(x),x$2)+4*diff(y(x),x)+4*y(x)=5*x*exp(-2*x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-2 x} \left (c_{2} +c_{1} x +\frac {5}{6} x^{3}\right ) \]
✓ Solution by Mathematica
Time used: 0.03 (sec). Leaf size: 29
DSolve[y''[x]+4*y'[x]+4*y[x]==5*x*Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{6} e^{-2 x} \left (5 x^3+6 c_2 x+6 c_1\right ) \]