Internal problem ID [11280]
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]]
\[ \boxed {y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y=\cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(y(x),x$4)-2*diff(y(x),x$2)+y(x)=cos(x),y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{4} x +c_{2} \right ) {\mathrm e}^{-x}+\left (c_{3} x +c_{1} \right ) {\mathrm e}^{x}+\frac {\cos \left (x \right )}{4} \]
✓ Solution by Mathematica
Time used: 0.131 (sec). Leaf size: 42
DSolve[y''''[x]-2*y''[x]+y[x]==Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\cos (x)}{4}+e^{-x} \left (c_2 x+c_3 e^{2 x}+c_4 e^{2 x} x+c_1\right ) \]