74.16.8 problem 8

Internal problem ID [16514]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.8, page 203
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 09:10:02 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (-2-2 x \right ) y^{\prime \prime }+2 y^{\prime }+4 y&=0 \end{align*}

Using series method with expansion around

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

Solution by Maple

Time used: 0.003 (sec). Leaf size: 47

Order:=6; 
dsolve((-2-2*x)*diff(y(x),x$2)+2*diff(y(x),x)+4*y(x)=0,y(x),type='series',x=0);
 
\[ y = \left (1+x^{2}+\frac {1}{6} x^{4}-\frac {1}{15} x^{5}\right ) y \left (0\right )+\left (x +\frac {1}{2} x^{2}+\frac {1}{3} x^{3}+\frac {1}{30} x^{5}\right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]

Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 52

AsymptoticDSolveValue[(-2-2*x)*D[y[x],{x,2}]+2*D[y[x],x]+4*y[x]==0,y[x],{x,0,"6"-1}]
 
\[ y(x)\to c_1 \left (-\frac {x^5}{15}+\frac {x^4}{6}+x^2+1\right )+c_2 \left (\frac {x^5}{30}+\frac {x^3}{3}+\frac {x^2}{2}+x\right ) \]