Internal problem ID [11269]
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]]
\[ \boxed {y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y={\mathrm e}^{x}+4} \]
✓ 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)=exp(x)+4,y(x), singsol=all)
\[ y \left (x \right ) = 4+\left (c_{4} x +c_{2} \right ) {\mathrm e}^{-x}+\frac {\left (3+2 x^{2}+4 \left (-1+4 c_{3} \right ) x +16 c_{1} \right ) {\mathrm e}^{x}}{16} \]
✓ Solution by Mathematica
Time used: 0.174 (sec). Leaf size: 47
DSolve[y''''[x]-2*y''[x]+y[x]==Exp[x]+4,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x \left (\frac {x^2}{8}+\left (-\frac {1}{4}+c_4\right ) x+\frac {3}{16}+c_3\right )+e^{-x} ((2+c_2) x+c_1)+4 \]