40.11.1 problem 26

Internal problem ID [6735]
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 : 26
Date solved : Monday, January 27, 2025 at 02:25:42 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y^{\prime }+y&={\mathrm e}^{3 x}+6 \,{\mathrm e}^{x}-3 \,{\mathrm e}^{-2 x}+5 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 55

dsolve(diff(y(x),x$2)+diff(y(x),x)+y(x)=exp(3*x)+6*exp(x)-3*exp(-2*x)+5,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 3.087 (sec). Leaf size: 70

DSolve[D[y[x],{x,2}]+D[y[x],x]+y[x]==Exp[3*x]+6*Exp[x]-3*Exp[-2*x]+5,y[x],x,IncludeSingularSolutions -> True]
 

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