44.3.31 problem 41

Internal problem ID [7012]
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 : 41
Date solved : Monday, January 27, 2025 at 02:40:55 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 )&=4\\ y^{\prime }\left (1\right )&=-2 \end{align*}

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 24

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

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

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 31

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

\[ y(x)\to -2 x+\frac {9 e^{1-x}}{2}+\frac {3}{2} e^{3 x-3} \]