Internal problem ID [10263]
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.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }-y-{\mathrm e}^{x} \cos \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(diff(y(x),x$4)-y(x)=exp(x)*cos(x),y(x), singsol=all)
\[ y \relax (x ) = -\frac {\cos \relax (x ) {\mathrm e}^{x}}{5}+\cos \relax (x ) c_{1}+{\mathrm e}^{x} c_{2}+c_{3} \sin \relax (x )+c_{4} {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.039 (sec). Leaf size: 38
DSolve[y''''[x]-y[x]==Exp[x]*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} 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) \\ \end{align*}