15.14.18 problem 18

Internal problem ID [3190]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 23, page 106
Problem number : 18
Date solved : Monday, January 27, 2025 at 07:25:47 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=x^{2}-8 \end{align*}

Solution by Maple

Time used: 0.004 (sec). Leaf size: 26

dsolve(diff(y(x),x$2)-diff(y(x),x)-2*y(x)=x^2-8,y(x), singsol=all)
 
\[ y = {\mathrm e}^{2 x} c_2 +{\mathrm e}^{-x} c_{1} -\frac {x^{2}}{2}+\frac {x}{2}+\frac {13}{4} \]

Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 36

DSolve[D[y[x],{x,2}]-D[y[x],x]-2*y[x]==x^2-8,y[x],x,IncludeSingularSolutions -> True]
 
\[ y(x)\to \frac {1}{4} \left (-2 x^2+2 x+13\right )+c_1 e^{-x}+c_2 e^{2 x} \]