Internal problem ID [5241]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 2. Linear equations with constant coefficients. Page 89
Problem number: 1(d).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y-{\mathrm e}^{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 35
dsolve(diff(y(x),x$4)-4*diff(y(x),x$3)+6*diff(y(x),x$2)-4*diff(y(x),x)+y(x)=exp(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{x} x^{4}}{24}+c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{x} x +c_{3} {\mathrm e}^{x} x^{2}+c_{4} {\mathrm e}^{x} x^{3} \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 39
DSolve[y''''[x]-4*y'''[x]+6*y''[x]-4*y'[x]+y[x]==Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{24} e^x \left (x^4+24 c_4 x^3+24 c_3 x^2+24 c_2 x+24 c_1\right ) \\ \end{align*}