44.3.32 problem 42

Internal problem ID [7013]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Review problems at page 34
Problem number : 42
Date solved : Sunday, March 30, 2025 at 11:34:00 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=6 x +4 \end{align*}

With initial conditions

\begin{align*} y \left (-1\right )&=0\\ y^{\prime }\left (-1\right )&=1 \end{align*}

✓ Maple. Time used: 0.055 (sec). Leaf size: 24

ode:=diff(diff(y(x),x),x)-2*diff(y(x),x)-3*y(x) = 6*x+4; 
ic:=y(-1) = 0, D(y)(-1) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -\frac {9 \,{\mathrm e}^{-1-x}}{4}+\frac {{\mathrm e}^{3+3 x}}{4}-2 x \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 29

ode=D[y[x],{x,2}]-2*D[y[x],x]-3*y[x]==6*x+4; 
ic={y[-1]==0,Derivative[1][y][-1] == 1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{4} \left (-8 x-9 e^{-x-1}+e^{3 x+3}\right ) \]

✓ Sympy. Time used: 0.248 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-6*x - 3*y(x) - 2*Derivative(y(x), x) + Derivative(y(x), (x, 2)) - 4,0) 
ics = {y(-1): 0, Subs(Derivative(y(x), x), x, -1): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - 2 x + \frac {e^{3} e^{3 x}}{4} - \frac {9 e^{- x}}{4 e} \]