Internal problem ID [11756]
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: 26.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+7 y^{\prime }+10 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = -4, y^{\prime }\left (0\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 17
dsolve([diff(y(x),x$2)+7*diff(y(x),x)+10*y(x)=0,y(0) = -4, D(y)(0) = 2],y(x), singsol=all)
\[ y \left (x \right ) = 2 \,{\mathrm e}^{-5 x}-6 \,{\mathrm e}^{-2 x} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 20
DSolve[{y''[x]+7*y'[x]+10*y[x]==0,{y[0]==-4,y'[0]==2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-5 x} \left (2-6 e^{3 x}\right ) \]