83.11.10 problem 10

Internal problem ID [21999]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Chapter VI. Linear equations with constant coefficients. Ex. XIII at page 106
Problem number : 10
Date solved : Thursday, October 02, 2025 at 08:21:32 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y+8 \,{\mathrm e}^{-x}+3 x&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 27

ode:=diff(diff(y(x),x),x)-2*diff(y(x),x)-3*y(x)+8*exp(-x)+3*x = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {2}{3}+\frac {\left (1+4 x +2 c_1 \right ) {\mathrm e}^{-x}}{2}+{\mathrm e}^{3 x} c_2 +x \]

✓ Mathematica. Time used: 0.12 (sec). Leaf size: 41

ode=D[y[x],{x,2}]-2*D[y[x],x]-3*y[x]+8*Exp[-x]+3*x==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{6} e^{-x} \left (12 x+e^x (6 x-4)+6 c_2 e^{4 x}+3+6 c_1\right ) \end{align*}

✓ Sympy. Time used: 0.153 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x - 3*y(x) - 2*Derivative(y(x), x) + Derivative(y(x), (x, 2)) + 8*exp(-x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{2} e^{3 x} + x + \left (C_{1} + 2 x\right ) e^{- x} - \frac {2}{3} \]