Internal problem ID [13253]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 15. General solutions to Homogeneous linear differential equations. Additional
exercises page 294
Problem number: 15.6 (a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-4 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve([diff(y(x),x$2)-4*y(x)=0,y(0) = 1, D(y)(0) = 0],y(x), singsol=all)
\[ y = \frac {{\mathrm e}^{2 x}}{2}+\frac {{\mathrm e}^{-2 x}}{2} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 21
DSolve[{y''[x]-4*y[x]==0,{y[0]==1,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^{-2 x} \left (e^{4 x}+1\right ) \]