73.8.37 problem 13.6 (c)

Internal problem ID [15245]
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 (c)
Date solved : Tuesday, January 28, 2025 at 07:50:47 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=8\\ y^{\prime }\left (0\right )&=5 \end{align*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 10

dsolve([diff(y(x),x$2)=diff(y(x),x),y(0) = 8, D(y)(0) = 5],y(x), singsol=all)
 

\[ y = 3+5 \,{\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 12

DSolve[{D[y[x],{x,2}]==D[y[x],x],{y[0]==8,Derivative[1][y][0] ==5}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 5 e^x+3 \]