Internal problem ID [5274]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 3. Linear equations with variable coefficients. Page 130
Problem number: 5.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-y x=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = 0, y^{\prime \prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 14
dsolve([diff(y(x),x$3)-x*y(x)=0,y(0) = 1, D(y)(0) = 0, (D@@2)(y)(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = \hypergeom \left (\left [\right ], \left [\frac {1}{2}, \frac {3}{4}\right ], \frac {x^{4}}{64}\right ) \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 21
DSolve[{y'''[x]-x*y[x]==0,{y[0]==1,y'[0]==0,y''[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \, _0F_2\left (;\frac {1}{2},\frac {3}{4};\frac {x^4}{64}\right ) \\ \end{align*}