Internal problem ID [10253]
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]]
\[ \boxed {y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y-\cos \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 38
dsolve(diff(y(x),x$4)+2*diff(y(x),x$2)+y(x)=cos(x),y(x), singsol=all)
\[ y \left (x \right ) = \left (-\frac {x^{2}}{8}+\frac {1}{4}\right ) \cos \left (x \right )+\frac {x \sin \left (x \right )}{8}+c_{1} \cos \left (x \right )+\sin \left (x \right ) c_{2} +c_{3} \sin \left (x \right ) x +c_{4} \cos \left (x \right ) x \]
✓ Solution by Mathematica
Time used: 0.042 (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*}