Internal problem ID [11764]
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: 34.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+6 y^{\prime }+58 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = -1, y^{\prime }\left (0\right ) = 5] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 23
dsolve([diff(y(x),x$2)+6*diff(y(x),x)+58*y(x)=0,y(0) = -1, D(y)(0) = 5],y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{-3 x} \left (2 \sin \left (7 x \right )-7 \cos \left (7 x \right )\right )}{7} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 27
DSolve[{y''[x]+6*y'[x]+58*y[x]==0,{y[0]==-1,y'[0]==5}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{7} e^{-3 x} (2 \sin (7 x)-7 \cos (7 x)) \]