Internal problem ID [4094]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 20. Constant coefficients
Problem number: Exercise 20, problem 32, page 220.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+4 y^{\prime }+4 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 14
dsolve([diff(y(x),x$2)+4*diff(y(x),x)+4*y(x)=0,y(0) = 1, D(y)(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-2 x} \left (1+3 x \right ) \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 16
DSolve[{y''[x]+4*y'[x]+4*y[x]==0,{y[0]==1,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-2 x} (3 x+1) \\ \end{align*}