7.15.16 problem 16

Internal problem ID [472]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 3. Power series methods. Section 3.3 (Regular singular points). Problems at page 231
Problem number : 16
Date solved : Monday, January 27, 2025 at 02:53:59 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{3} \left (1-x \right ) y^{\prime \prime }+\left (3 x +2\right ) y^{\prime }+y x&=0 \end{align*}

Using series method with expansion around

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

✗ Solution by Maple

Order:=6; 
dsolve(x^3*(1-x)*diff(y(x),x$2)+(3*x+2)*diff(y(x),x)+x*y(x)=0,y(x),type='series',x=0);
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.048 (sec). Leaf size: 80

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

\[ y(x)\to c_1 \left (-\frac {3 x^4}{16}+\frac {x^3}{4}-\frac {x^2}{4}+1\right )+\frac {c_2 e^{\frac {1}{x^2}+\frac {5}{x}} \left (-\frac {8921 x^5}{16}+\frac {1629 x^4}{8}-\frac {311 x^3}{4}+28 x^2-\frac {15 x}{2}+1\right )}{x^2} \]