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 : Monday, January 27, 2025 at 02:40:57 PM
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*}

✓ Solution by Maple

Time used: 0.029 (sec). Leaf size: 24

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

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

✓ Solution by Mathematica

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

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

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