82.33.17 problem Ex. 17

Internal problem ID [18910]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VI. Linear equations with constant coefficients. Examples on chapter VI, page 80
Problem number : Ex. 17
Date solved : Tuesday, January 28, 2025 at 12:34:15 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 31

dsolve(diff(y(x),x$4)-y(x)=exp(x)*cos(x),y(x), singsol=all)
 

\[ y \left (x \right ) = c_4 \,{\mathrm e}^{-x}+\frac {\left (5 c_{1} -{\mathrm e}^{x}\right ) \cos \left (x \right )}{5}+c_{2} {\mathrm e}^{x}+c_3 \sin \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 38

DSolve[D[y[x],{x,4}]-y[x]==Exp[x]*Cos[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 e^x+c_3 e^{-x}+\left (-\frac {e^x}{5}+c_2\right ) \cos (x)+c_4 \sin (x) \]