7.16.8 problem 8

Internal problem ID [505]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 3. Power series methods. Section 3.4 (Method of Frobenius: The exceptional cases). Problems at page 246
Problem number : 8
Date solved : Monday, January 27, 2025 at 02:54:13 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 42

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

\[ y = c_1 \,x^{4} \left (1+2 x +3 x^{2}+4 x^{3}+5 x^{4}+6 x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_2 \left (-144-96 x -48 x^{2}+48 x^{4}+96 x^{5}+\operatorname {O}\left (x^{6}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.044 (sec). Leaf size: 40

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

\[ y(x)\to c_1 \left (x^2+\frac {1}{x^2}-4 x-\frac {4}{x}+6\right )+c_2 \left (\frac {x^2}{6}-\frac {2 x}{3}+1\right ) \]