7.13.2 problem 2

Internal problem ID [401]
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 : 2
Date solved : Monday, January 27, 2025 at 02:53:24 AM
CAS classification : [_quadrature]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 37

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

\[ y = \left (1+4 x +8 x^{2}+\frac {32}{3} x^{3}+\frac {32}{3} x^{4}+\frac {128}{15} x^{5}\right ) y \left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 37

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

\[ y(x)\to c_1 \left (\frac {128 x^5}{15}+\frac {32 x^4}{3}+\frac {32 x^3}{3}+8 x^2+4 x+1\right ) \]