50.13.19 problem 18

Internal problem ID [8034]
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
Date solved : Monday, January 27, 2025 at 03:36:59 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=1 \end{align*}

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: 0.014 (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)
 

\[ y = -\frac {{\mathrm e}^{-x}}{2}+\frac {9 \,{\mathrm e}^{x}}{2}-x \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 25

DSolve[{D[y[x],{x,3}]-D[y[x],x]==1,{y[0]==4,Derivative[1][y][0] ==4,Derivative[2][y][0] ==4}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -x-\frac {e^{-x}}{2}+\frac {9 e^x}{2} \]