Internal problem ID [4700]
Book: Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill
2014
Section: Chapter 24. Solutions of linear DE by Laplace transforms. Supplementary Problems. page
248
Problem number: Problem 24.31.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y^{\prime }+y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 4, y^{\prime }\relax (0) = -3] \end {align*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 31
dsolve([diff(y(x),x$2)+diff(y(x),x)+y(x)=0,y(0) = 4, D(y)(0) = -3],y(x), singsol=all)
\[ y \relax (x ) = -\frac {2 \,{\mathrm e}^{-\frac {x}{2}} \left (\sqrt {3}\, \sin \left (\frac {\sqrt {3}\, x}{2}\right )-6 \cos \left (\frac {\sqrt {3}\, x}{2}\right )\right )}{3} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 47
DSolve[{y''[x]+y'[x]+y[x]==0,{y[0]==4,y'[0]==-3}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {2}{3} e^{-x/2} \left (\sqrt {3} \sin \left (\frac {\sqrt {3} x}{2}\right )-6 \cos \left (\frac {\sqrt {3} x}{2}\right )\right ) \\ \end{align*}