40.11.8 problem 33

Internal problem ID [6742]
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 : 33
Date solved : Monday, January 27, 2025 at 02:27:03 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y&={\mathrm e}^{x}+{\mathrm e}^{-x}+\sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 46

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

\[ y = \frac {\left (2 x +4 c_3 +2\right ) {\mathrm e}^{-x}}{4}+\frac {\left (4 c_2 -x +1\right ) \sin \left (x \right )}{4}+\frac {\left (4 c_1 -x \right ) \cos \left (x \right )}{4}+\frac {{\mathrm e}^{x}}{4} \]

✓ Solution by Mathematica

Time used: 0.219 (sec). Leaf size: 55

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

\[ y(x)\to \frac {1}{8} \left (2 e^{-x} \left (2 x+e^{2 x}+2+4 c_3\right )+(-2 x-1+8 c_1) \cos (x)+(-2 x+3+8 c_2) \sin (x)\right ) \]