Internal problem ID [14791]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.8, page 203
Problem number: 15.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {y^{\prime \prime }-4 x^{2} y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 0] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 12
Order:=6; dsolve([diff(y(x),x$2)-4*x^2*y(x)=0,y(0) = 1, D(y)(0) = 0],y(x),type='series',x=0);
\[ y \left (x \right ) = 1+\frac {1}{3} x^{4}+\operatorname {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 12
AsymptoticDSolveValue[{y''[x]-4*x^2*y[x]==0,{y[0]==1,y'[0]==0}},y[x],{x,0,5}]
\[ y(x)\to \frac {x^4}{3}+1 \]