7.13.8 problem 8

Internal problem ID [407]
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 : 8
Date solved : Monday, January 27, 2025 at 02:53:26 AM
CAS classification : [_separable]

\begin{align*} 2 \left (1+x \right ) y^{\prime }+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*(x+1)*diff(y(x),x)+y(x)=0,y(x),type='series',x=0);
 

\[ y = \left (1-\frac {1}{2} x +\frac {3}{8} x^{2}-\frac {5}{16} x^{3}+\frac {35}{128} x^{4}-\frac {63}{256} x^{5}\right ) y \left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

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

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

\[ y(x)\to c_1 \left (-\frac {63 x^5}{256}+\frac {35 x^4}{128}-\frac {5 x^3}{16}+\frac {3 x^2}{8}-\frac {x}{2}+1\right ) \]