Internal problem ID [6366]
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]]
\[ \boxed {y^{\prime \prime \prime }-y^{\prime }=1} \] With initial conditions \begin {align*} [y \left (0\right ) = 4, y^{\prime }\left (0\right ) = 4, y^{\prime \prime }\left (0\right ) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.031 (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)
\[ y \left (x \right ) = -\frac {{\mathrm e}^{-x}}{2}+\frac {9 \,{\mathrm e}^{x}}{2}-x \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 25
DSolve[{y'''[x]-y'[x]==1,{y[0]==4,y'[0]==4,y''[0]==4}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -x-\frac {e^{-x}}{2}+\frac {9 e^x}{2} \]