Internal problem ID [11271]
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]]
\[ \boxed {y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y=\cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(diff(y(x),x$4)+2*diff(y(x),x$2)+y(x)=cos(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (8 c_{4} x -x^{2}+8 c_{1} +2\right ) \cos \left (x \right )}{8}+\left (\left (c_{3} +\frac {1}{8}\right ) x +c_{2} \right ) \sin \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.065 (sec). Leaf size: 43
DSolve[y''''[x]+2*y''[x]+y[x]==Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \left (-\frac {x^2}{8}+c_2 x+\frac {5}{16}+c_1\right ) \cos (x)+\frac {1}{4} (x+4 c_4 x+4 c_3) \sin (x) \]