73.23.29 problem 33.11 (c)

Internal problem ID [15675]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 33. Power series solutions I: Basic computational methods. Additional Exercises. page 641
Problem number : 33.11 (c)
Date solved : Tuesday, January 28, 2025 at 08:04:01 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+{\mathrm e}^{2 x} y&=0 \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 34

Order:=4; 
dsolve(diff(y(x),x$2)+exp(2*x)*y(x)=0,y(x),type='series',x=0);
 

\[ y = \left (1-\frac {1}{2} x^{2}-\frac {1}{3} x^{3}\right ) y \left (0\right )+\left (x -\frac {1}{6} x^{3}\right ) y^{\prime }\left (0\right )+O\left (x^{4}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 35

AsymptoticDSolveValue[D[y[x],{x,2}]+Exp[2*x]*y[x]==0,y[x],{x,0,"4"-1}]
 

\[ y(x)\to c_2 \left (x-\frac {x^3}{6}\right )+c_1 \left (-\frac {x^3}{3}-\frac {x^2}{2}+1\right ) \]