Internal problem ID [5227]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 2. Linear equations with constant coefficients. Page 79
Problem number: 1(c).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-4 y^{\prime }=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 1, y^{\prime \prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.013 (sec). Leaf size: 17
dsolve([diff(y(x),x$3)-4*diff(y(x),x)=0,y(0) = 0, D(y)(0) = 1, (D@@2)(y)(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{2 x}}{4}-\frac {{\mathrm e}^{-2 x}}{4} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 69
DSolve[{y'''[x]-4*y[x]==0,{y[0]==0,y'[0]==1,y''[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{-\frac {x}{\sqrt [3]{2}}} \left (e^{\frac {3 x}{\sqrt [3]{2}}}+\sqrt {3} \sin \left (\frac {\sqrt {3} x}{\sqrt [3]{2}}\right )-\cos \left (\frac {\sqrt {3} x}{\sqrt [3]{2}}\right )\right )}{3\ 2^{2/3}} \\ \end{align*}