81.5.4 problem 4

Internal problem ID [18667]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter IV. Ordinary linear differential equations with constant coefficients. Exercises at page 58
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 12:09:03 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 31

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

\[ y \left (x \right ) = {\mathrm e}^{\frac {\left (-3+\sqrt {13}\right ) x}{2}} c_{2} +{\mathrm e}^{-\frac {\left (3+\sqrt {13}\right ) x}{2}} c_{1} +\frac {{\mathrm e}^{x}}{3} \]

✓ Solution by Mathematica

Time used: 0.124 (sec). Leaf size: 55

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

\[ y(x)\to \frac {1}{3} e^{-\frac {1}{2} \left (3+\sqrt {13}\right ) x} \left (e^{\frac {1}{2} \left (5+\sqrt {13}\right ) x}+3 c_2 e^{\sqrt {13} x}+3 c_1\right ) \]