22.3 problem Ex 3

Internal problem ID [10235]

Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section: Chapter VII, Linear differential equations with constant coefficients. Article 44. Roots of auxiliary equation repeated. Page 94
Problem number: Ex 3.
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 }+2 y^{\prime \prime \prime }-2 y^{\prime }-y=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 31

dsolve(diff(y(x),x$4)+2*diff(y(x),x$3)-2*diff(y(x),x)-y(x)=0,y(x), singsol=all)
 

\[ y \relax (x ) = c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{-x}+c_{3} {\mathrm e}^{-x} x +c_{4} {\mathrm e}^{-x} x^{2} \]

Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 30

DSolve[y''''[x]+2*y'''[x]-2*y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to e^{-x} (x (c_3 x+c_2)+c_1)+c_4 e^x \\ \end{align*}