Internal problem ID [165]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.1, second order linear equations. Page 299
Problem number: 9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 y^{\prime }+y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2, y^{\prime }\relax (0) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 12
dsolve([diff(y(x),x$2)+2*diff(y(x),x)+y(x)=0,y(0) = 2, D(y)(0) = -1],y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-x} \left (2+x \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 14
DSolve[{y''[x]+2*y'[x]+y[x]==0,{y[0]==2,y'[0]==-1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x} (x+2) \\ \end{align*}