82.28.1 problem Ex. 1

Internal problem ID [18880]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VI. Linear equations with constant coefficients. problems at page 75
Problem number : Ex. 1
Date solved : Tuesday, January 28, 2025 at 12:33:20 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }+y&=3+{\mathrm e}^{-x}+5 \,{\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 54

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

\[ y \left (x \right ) = \frac {\left (3 c_{2} {\mathrm e}^{\frac {3 x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right )+3 c_3 \,{\mathrm e}^{\frac {3 x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right )+x +3 c_{1} +9 \,{\mathrm e}^{x}+\frac {5 \,{\mathrm e}^{3 x}}{3}+1\right ) {\mathrm e}^{-x}}{3} \]

✓ Solution by Mathematica

Time used: 1.836 (sec). Leaf size: 79

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

\[ y(x)\to \frac {1}{9} e^{-x} \left (3 x+27 e^x+5 e^{3 x}+9 c_3 e^{3 x/2} \cos \left (\frac {\sqrt {3} x}{2}\right )+9 c_2 e^{3 x/2} \sin \left (\frac {\sqrt {3} x}{2}\right )+3+9 c_1\right ) \]