Internal problem ID [11761]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.2. The homogeneous linear equation with constant coefficients.
Exercises page 135
Problem number: 31.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }+4 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = 7] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve([diff(y(x),x$2)+4*diff(y(x),x)+4*y(x)=0,y(0) = 3, D(y)(0) = 7],y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-2 x} \left (3+13 x \right ) \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 16
DSolve[{y''[x]+4*y'[x]+4*y[x]==0,{y[0]==3,y'[0]==7}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-2 x} (13 x+3) \]