Internal problem ID [5613]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Section 2.7. HIGHER ORDER LINEAR EQUATIONS, COUPLED HARMONIC
OSCILLATORS Page 98
Problem number: 18.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-y^{\prime }-1=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 4, y^{\prime }\relax (0) = 4, y^{\prime \prime }\relax (0) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 18
dsolve([diff(y(x),x$3)-diff(y(x),x)=1,y(0) = 4, D(y)(0) = 4, (D@@2)(y)(0) = 4],y(x), singsol=all)
\[ y \relax (x ) = -\frac {{\mathrm e}^{-x}}{2}+\frac {9 \,{\mathrm e}^{x}}{2}-x \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 17
DSolve[{y'''[x]-y'[x]==1,{y[0]==4,y'[0]==4,y''[0]==4}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x+5 \sinh (x)+4 \cosh (x) \\ \end{align*}