7.13.19 problem 19

Internal problem ID [418]
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 : 19
Date solved : Monday, January 27, 2025 at 02:53:30 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 )&=0\\ y^{\prime }\left (0\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 14

Order:=6; 
dsolve([diff(y(x),x$2)+4*y(x)=0,y(0) = 0, D(y)(0) = 3],y(x),type='series',x=0);
 

\[ y = 3 x -2 x^{3}+\frac {2}{5} x^{5}+\operatorname {O}\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 19

AsymptoticDSolveValue[{D[y[x],{x,2}]+4*y[x]==0,{y[0]==0,Derivative[1][y][0] ==3}},y[x],{x,0,"6"-1}]
 

\[ y(x)\to \frac {2 x^5}{5}-2 x^3+3 x \]