62.29.2 problem Ex 2

Internal problem ID [12953]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter VII, Linear differential equations with constant coefficients. Article 52. Summary. Page 117
Problem number : Ex 2
Date solved : Tuesday, January 28, 2025 at 04:45:13 AM
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: 0.007 (sec). Leaf size: 31

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

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

✓ Solution by Mathematica

Time used: 0.057 (sec). Leaf size: 120

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

\[ y(x)\to e^x \int _1^x\frac {1}{4} \cos (K[1])dK[1]+e^{-x} \int _1^x-\frac {1}{4} e^{2 K[3]} \cos (K[3])dK[3]+\sin (x) \int _1^x-\frac {1}{2} e^{K[4]} \cos ^2(K[4])dK[4]+\cos (x) \int _1^x\frac {1}{4} e^{K[2]} \sin (2 K[2])dK[2]+c_1 e^x+c_3 e^{-x}+c_2 \cos (x)+c_4 \sin (x) \]