Internal problem ID [13282]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 17. Second order Homogeneous equations with constant coefficients. Additional
exercises page 334
Problem number: 17.4 (f).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {4 y^{\prime \prime }+4 y^{\prime }+y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 6, y^{\prime }\left (0\right ) = -5] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 13
dsolve([4*diff(y(x),x$2)+4*diff(y(x),x)+y(x)=0,y(0) = 6, D(y)(0) = -5],y(x), singsol=all)
\[ y = -2 \,{\mathrm e}^{-\frac {x}{2}} \left (-3+x \right ) \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 17
DSolve[{4*y''[x]+4*y'[x]+y[x]==0,{y[0]==6,y'[0]==-5}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -2 e^{-x/2} (x-3) \]