7.13.3 problem 3

Internal problem ID [402]
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 : 3
Date solved : Monday, January 27, 2025 at 02:53:24 AM
CAS classification : [_quadrature]

\begin{align*} 2 y^{\prime }+3 y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 37

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

\[ y = \left (1-\frac {3}{2} x +\frac {9}{8} x^{2}-\frac {9}{16} x^{3}+\frac {27}{128} x^{4}-\frac {81}{1280} x^{5}\right ) y \left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 41

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

\[ y(x)\to c_1 \left (-\frac {81 x^5}{1280}+\frac {27 x^4}{128}-\frac {9 x^3}{16}+\frac {9 x^2}{8}-\frac {3 x}{2}+1\right ) \]