15.12.7 problem 7

Internal problem ID [3151]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 20, page 90
Problem number : 7
Date solved : Monday, January 27, 2025 at 07:23:51 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-y&=3 x +5 \,{\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 26

dsolve(diff(y(x),x$2)-y(x)=3*x+5*exp(x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{-x} c_{1} +\frac {\left (10 x +4 c_2 -5\right ) {\mathrm e}^{x}}{4}-3 x \]

✓ Solution by Mathematica

Time used: 0.212 (sec). Leaf size: 32

DSolve[D[y[x],{x,2}]-y[x]==3*x+5*Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -3 x+e^x \left (\frac {5 x}{2}-\frac {5}{4}+c_1\right )+c_2 e^{-x} \]