Internal problem ID [13509]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 8, y^{\prime }\left (0\right ) = 5] \end {align*}
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = 3+5 \,{\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 12
DSolve[{y''[x]==y'[x],{y[0]==8,y'[0]==5}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 5 e^x+3 \]