Internal problem ID [287]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 5.3, Higher-Order Linear Differential Equations. Homogeneous Equations with
Constant Coefficients. Page 300
Problem number: problem 12.
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 }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve(diff(y(x),x$4)-3*diff(y(x),x$3)+3*diff(y(x),x$2)-diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1}+c_{2} {\mathrm e}^{x}+c_{3} {\mathrm e}^{x} x +c_{4} {\mathrm e}^{x} x^{2} \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 31
DSolve[y''''[x]-3*y'''[x]+3*y''[x]-y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x (c_2 (x-1)+c_3 ((x-2) x+2)+c_1)+c_4 \\ \end{align*}