9.7.12 problem problem 12

Internal problem ID [1053]
Book : Differential equations and linear algebra, 4th ed., Edwards and Penney
Section : Chapter 11 Power series methods. Section 11.1 Introduction and Review of power series. Page 615
Problem number : problem 12
Date solved : Monday, January 27, 2025 at 04:32:35 AM
CAS classification : [[_2nd_order, _missing_x]]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 39

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

\[ y = \left (1+2 x^{2}+\frac {2}{3} x^{4}\right ) y \left (0\right )+\left (x +\frac {2}{3} x^{3}+\frac {2}{15} x^{5}\right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 40

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

\[ y(x)\to c_2 \left (\frac {2 x^5}{15}+\frac {2 x^3}{3}+x\right )+c_1 \left (\frac {2 x^4}{3}+2 x^2+1\right ) \]