9.7.8 problem problem 8

Internal problem ID [1049]
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 8
Date solved : Monday, January 27, 2025 at 04:29:19 AM
CAS classification : [_separable]

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

\[ y = \left (1+\frac {1}{2} x -\frac {1}{8} x^{2}+\frac {1}{16} x^{3}-\frac {5}{128} x^{4}+\frac {7}{256} x^{5}\right ) y \left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

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

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

\[ y(x)\to c_1 \left (\frac {7 x^5}{256}-\frac {5 x^4}{128}+\frac {x^3}{16}-\frac {x^2}{8}+\frac {x}{2}+1\right ) \]