Internal problem ID [13561]
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: 15.2 (b).
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 ) = 0, y^{\prime }\left (0\right ) = 12] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 17
dsolve([diff(y(x),x$2)-4*y(x)=0,y(0) = 0, D(y)(0) = 12],y(x), singsol=all)
\[ y \left (x \right ) = 3 \,{\mathrm e}^{2 x}-3 \,{\mathrm e}^{-2 x} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 19
DSolve[{y''[x]-4*y[x]==0,{y[0]==0,y'[0]==12}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 3 e^{-2 x} \left (e^{4 x}-1\right ) \]