Internal problem ID [824]
Book: Elementary differential equations and boundary value problems, 11th ed., Boyce, DiPrima,
Meade
Section: Chapter 4.2, Higher order linear differential equations. Constant coefficients. page
180
Problem number: 10.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+4 y^{\prime \prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 22
dsolve(diff(y(x),x$4)-4*diff(y(x),x$3)+4*diff(y(x),x$2)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1}+c_{2} x +c_{3} {\mathrm e}^{2 x}+c_{4} {\mathrm e}^{2 x} x \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 22
DSolve[y''''[x]-4*y'''[x]+4*y'''[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x (x (c_4 x+c_3)+c_2)+c_1 \\ \end{align*}