Internal problem ID [1771]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.8, Series solutions. Page 195
Problem number: 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-t^{3} y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = -2] \end {align*}
With the expansion point for the power series method at \(t = 0\).
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 10
Order:=6; dsolve([diff(y(t),t$2)-t^3*y(t)=0,y(0) = 0, D(y)(0) = -2],y(t),type='series',t=0);
\[ y \relax (t ) = \left (-2\right ) t +\mathrm {O}\left (t^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 6
AsymptoticDSolveValue[{y''[t]-t^3*y[t]==0,{y[0]==0,y'[0]==-2}},y[t],{t,0,5}]
\[ y(t)\to -2 t \]