Internal problem ID [11766]
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: 36.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+5 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 2, y^{\prime }\left (0\right ) = 6] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve([diff(y(x),x$2)+2*diff(y(x),x)+5*y(x)=0,y(0) = 2, D(y)(0) = 6],y(x), singsol=all)
\[ y \left (x \right ) = 2 \,{\mathrm e}^{-x} \left (2 \sin \left (2 x \right )+\cos \left (2 x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 23
DSolve[{y''[x]+2*y'[x]+5*y[x]==0,{y[0]==2,y'[0]==6}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 2 e^{-x} (2 \sin (2 x)+\cos (2 x)) \]