Internal problem ID [10257]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter VII, Linear differential equations with constant coefficients. Article 50. Method of
undetermined coefficients. Page 107
Problem number: Ex 9.
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 }+2 y^{\prime \prime }+y-\cos \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 38
dsolve(diff(y(x),x$4)+2*diff(y(x),x$2)+y(x)=cos(x),y(x), singsol=all)
\[ y \relax (x ) = \left (-\frac {x^{2}}{8}+\frac {1}{4}\right ) \cos \relax (x )+\frac {3 \sin \relax (x ) x}{8}+\cos \relax (x ) c_{1}+\sin \relax (x ) c_{2}+c_{3} \cos \relax (x ) x +c_{4} \sin \relax (x ) x \]
✓ Solution by Mathematica
Time used: 0.037 (sec). Leaf size: 43
DSolve[y''''[x]+2*y''[x]+y[x]==Cos[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \left (-\frac {x^2}{8}+c_2 x+\frac {5}{16}+c_1\right ) \cos (x)+\frac {1}{4} (x+4 c_4 x+4 c_3) \sin (x) \\ \end{align*}