Internal problem ID [11765]
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: 35.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+6 y^{\prime }+13 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 22
dsolve([diff(y(x),x$2)+6*diff(y(x),x)+13*y(x)=0,y(0) = 3, D(y)(0) = -1],y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-3 x} \left (4 \sin \left (2 x \right )+3 \cos \left (2 x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 24
DSolve[{y''[x]+6*y'[x]+13*y[x]==0,{y[0]==3,y'[0]==-1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-3 x} (4 \sin (2 x)+3 \cos (2 x)) \]