81.5.12 problem 12

Internal problem ID [18675]
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 : 12
Date solved : Tuesday, January 28, 2025 at 12:09:17 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 33

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

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

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 40

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

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