82.48.15 problem Ex. 15

Internal problem ID [18996]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VIII. End of chapter problems at page 107
Problem number : Ex. 15
Date solved : Tuesday, January 28, 2025 at 12:44:46 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.048 (sec). Leaf size: 24

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

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