78.15.19 problem 21

Internal problem ID [18375]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 22. Higher Order Linear Equations. Coupled Harmonic Oscillators. Problems at page 160
Problem number : 21
Date solved : Tuesday, January 28, 2025 at 11:48:29 AM
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: 0.018 (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)
 

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

✓ 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]
 

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