Internal problem ID [10251]
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 7.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y-{\mathrm e}^{x}-4=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 44
dsolve(diff(y(x),x$4)-2*diff(y(x),x$2)+y(x)=exp(x)+4,y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{x} x^{2}}{8}-\frac {x \,{\mathrm e}^{x}}{4}+4+\frac {3 \,{\mathrm e}^{x}}{16}+c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{-x}+c_{3} x \,{\mathrm e}^{x}+c_{4} {\mathrm e}^{-x} x \]
✓ Solution by Mathematica
Time used: 0.108 (sec). Leaf size: 45
DSolve[y''''[x]-2*y''[x]+y[x]==Exp[x]+4,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x} ((2+c_2) x+c_1)+\frac {1}{16} e^x (2 x (x-2+8 c_4)+3+16 c_3)+4 \\ \end{align*}