82.30.1 problem Ex. 1

Internal problem ID [18885]
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 77
Problem number : Ex. 1
Date solved : Tuesday, January 28, 2025 at 12:33:23 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=\cos \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 31

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

\[ y \left (x \right ) = \left (c_3 x +c_{2} \right ) {\mathrm e}^{-x}+{\mathrm e}^{x} c_{1} -\frac {\cos \left (2 x \right )}{25}-\frac {2 \sin \left (2 x \right )}{25} \]

✓ Solution by Mathematica

Time used: 0.119 (sec). Leaf size: 43

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

\[ y(x)\to -\frac {2}{25} \sin (2 x)-\frac {1}{25} \cos (2 x)+e^{-x} \left (c_2 x+c_3 e^{2 x}+c_1\right ) \]