20.7.8 problem Problem 32

Internal problem ID [3723]
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 32
Date solved : Monday, January 27, 2025 at 07:56:13 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=2 \,{\mathrm e}^{-x}+3 \,{\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 36

dsolve(diff(y(x),x$3)+3*diff(y(x),x$2)+3*diff(y(x),x)+y(x)=2*exp(-x)+3*exp(2*x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left (9 c_3 \,x^{2}+3 x^{3}+9 c_{2} x +9 c_{1} \right ) {\mathrm e}^{-x}}{9}+\frac {{\mathrm e}^{2 x}}{9} \]

✓ Solution by Mathematica

Time used: 0.105 (sec). Leaf size: 41

DSolve[D[y[x],{x,3}]+3*D[y[x],{x,2}]+3*D[y[x],x]+y[x]==2*Exp[-x]+3*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{9} e^{-x} \left (3 x^3+9 c_3 x^2+e^{3 x}+9 c_2 x+9 c_1\right ) \]