83.1.4 problem 2 (d)

Internal problem ID [21909]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Chapter II. Definitions and fundamentals
Problem number : 2 (d)
Date solved : Thursday, October 02, 2025 at 08:09:16 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+y^{\prime }&=6 y+5 \,{\mathrm e}^{2 x} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 19

ode:=diff(diff(y(x),x),x)+diff(y(x),x) = 6*y(x)+5*exp(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-3 x} \left (\left (c_2 +x \right ) {\mathrm e}^{5 x}+c_1 \right ) \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 27

ode=D[y[x],{x,2}]+D[y[x],x]==6*y[x]+5*Exp[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 e^{-3 x}+e^{2 x} \left (x-\frac {1}{5}+c_2\right ) \end{align*}

✓ Sympy. Time used: 0.109 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-6*y(x) - 5*exp(2*x) + Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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