Internal problem ID [1777]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.8, Series solutions. Page 195
Problem number: 12(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
\[ \boxed {y^{\prime \prime }+y^{\prime } t^{3}+3 y t^{2}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
With the expansion point for the power series method at \(t = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 5
Order:=6; dsolve([diff(y(t),t$2)+t^3*diff(y(t),t)+3*t^2*y(t)=0,y(0) = 0, D(y)(0) = 0],y(t),type='series',t=0);
\[ y \left (t \right ) = 0 \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 4
AsymptoticDSolveValue[{y''[t]+t^3*y'[t]+3*t^2*y[t]==0,{y[0]==0,y'[0]==0}},y[t],{t,0,5}]
\[ y(t)\to 0 \]