44.3.29 problem 39

Internal problem ID [7010]
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 : 39
Date solved : Monday, January 27, 2025 at 02:40:52 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 (0\right )&=0\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 20

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

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

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 27

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

\[ y(x)\to \frac {1}{2} e^{-x} \left (-4 e^x x+e^{4 x}-1\right ) \]