Internal problem ID [10262]
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 6.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y-\cos \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(diff(y(x),x$4)-2*diff(y(x),x$2)+y(x)=cos(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\cos \left (x \right )}{4}+c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{-x}+c_{3} x \,{\mathrm e}^{x}+c_{4} {\mathrm e}^{-x} x \]
✓ Solution by Mathematica
Time used: 0.085 (sec). Leaf size: 36
DSolve[y''''[x]-2*y''[x]+y[x]==Cos[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\cos (x)}{4}+e^{-x} (c_2 x+c_1)+e^x (c_4 x+c_3) \\ \end{align*}