1.40 problem 41

Internal problem ID [6330]

Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 41.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _missing_x]]

\[ \boxed {y^{\prime \prime }+2 y^{\prime }+y=0} \]

Solution by Maple

Time used: 0.0 (sec). Leaf size: 18

dsolve(diff(y(x),x$2)+2*diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = {\mathrm e}^{-x} c_{1} +c_{2} {\mathrm e}^{-x} x \]

Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 18

DSolve[y''[x]+2*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to e^{-x} (c_2 x+c_1) \\ \end{align*}