Internal problem ID [4703]
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 24.35.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-y-5=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 0, y^{\prime \prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.017 (sec). Leaf size: 23
dsolve([diff(y(x),x$3)-y(x)=5,y(0) = 0, D(y)(0) = 0, (D@@2)(y)(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = -5+\frac {5 \,{\mathrm e}^{x}}{3}+\frac {10 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right )}{3} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 34
DSolve[{y'''[x]-y[x]==5,{y[0]==0,y'[0]==0,y''[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {5}{3} \left (e^x+2 e^{-x/2} \cos \left (\frac {\sqrt {3} x}{2}\right )-3\right ) \\ \end{align*}