73.8.39 problem 13.6 (e)

Internal problem ID [15247]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 13. Higher order equations: Extending first order concepts. Additional exercises page 259
Problem number : 13.6 (e)
Date solved : Tuesday, January 28, 2025 at 07:50:51 AM
CAS classification : [[_3rd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=10\\ y^{\prime }\left (0\right )&=5\\ y^{\prime \prime }\left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 13

dsolve([diff(y(x),x$3)=diff(y(x),x$2),y(0) = 10, D(y)(0) = 5, (D@@2)(y)(0) = 2],y(x), singsol=all)
 

\[ y = 8+3 x +2 \,{\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 15

DSolve[{D[y[x],{x,3}]==D[y[x],{x,2}],{y[0]==10,Derivative[1][y][0] ==5,Derivative[2][y][0] ==2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 3 x+2 e^x+8 \]