7.13.20 problem 20

Internal problem ID [419]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 3. Power series methods. Section 3.1 (Introduction). Problems at page 206
Problem number : 20
Date solved : Monday, January 27, 2025 at 02:53:31 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-4 y&=0 \end{align*}

Using series method with expansion around

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

With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

Order:=6; 
dsolve([diff(y(x),x$2)-4*y(x)=0,y(0) = 2, D(y)(0) = 0],y(x),type='series',x=0);
 

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

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 17

AsymptoticDSolveValue[{D[y[x],{x,2}]-4*y[x]==0,{y[0]==2,Derivative[1][y][0] ==0}},y[x],{x,0,"6"-1}]
 

\[ y(x)\to \frac {4 x^4}{3}+4 x^2+2 \]