40.11.2 problem 27

Internal problem ID [6736]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 16. Linear equations with constant coefficients (Short methods). Supplemetary problems. Page 107
Problem number : 27
Date solved : Monday, January 27, 2025 at 02:26:50 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 20

dsolve(diff(y(x),x$2)-y(x)=exp(x),y(x), singsol=all)
 

\[ y = c_2 \,{\mathrm e}^{-x}+\frac {{\mathrm e}^{x} \left (x +2 c_1 \right )}{2} \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 29

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

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