74.1.1 problem 1

Internal problem ID [15781]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 08:07:04 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 39

dsolve(diff(y(x),x$2)+diff(y(x),x)-2*y(x)=x^3,y(x), singsol=all)
 

\[ y = -\frac {{\mathrm e}^{-2 x} \left (\left (x^{3}+\frac {3}{2} x^{2}+\frac {9}{2} x +\frac {15}{4}\right ) {\mathrm e}^{2 x}-2 \,{\mathrm e}^{3 x} c_{1} -2 c_{2} \right )}{2} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 39

DSolve[D[y[x],{x,2}]+D[y[x],x]-2*y[x]==x^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{8} \left (-4 x^3-6 x^2-18 x-15\right )+c_1 e^{-2 x}+c_2 e^x \]