20.28.6 problem 6

Internal problem ID [4068]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 11, Series Solutions to Linear Differential Equations. Additional problems. Section 11.7. page 788
Problem number : 6
Date solved : Monday, January 27, 2025 at 08:07:26 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 x y^{\prime \prime }+5 \left (1-2 x \right ) y^{\prime }-5 y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 36

Order:=6; 
dsolve(2*x*diff(y(x),x$2)+5*(1-2*x)*diff(y(x),x)-5*y(x)=0,y(x),type='series',x=0);
 

\[ y \left (x \right ) = \frac {c_{1} \left (1+10 x +\operatorname {O}\left (x^{6}\right )\right )}{x^{{3}/{2}}}+c_{2} \left (1+x +\frac {15}{14} x^{2}+\frac {125}{126} x^{3}+\frac {625}{792} x^{4}+\frac {625}{1144} x^{5}+\operatorname {O}\left (x^{6}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 51

AsymptoticDSolveValue[2*x*D[y[x],{x,2}]+5*(1-2*x)*D[y[x],x]-5*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to \frac {c_2 (10 x+1)}{x^{3/2}}+c_1 \left (\frac {625 x^5}{1144}+\frac {625 x^4}{792}+\frac {125 x^3}{126}+\frac {15 x^2}{14}+x+1\right ) \]