78.21.5 problem 4 (c)

Internal problem ID [18449]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 5. Power Series Solutions and Special Functions. Section 31. Gauss Hypergeometric Equation. Problems at page 240
Problem number : 4 (c)
Date solved : Tuesday, January 28, 2025 at 11:50:15 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} x \left (1-x \right ) y^{\prime \prime }+\left (1-3 x \right ) y^{\prime }-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: 31

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

\[ y = \left (x^{5}+x^{4}+x^{3}+x^{2}+x +1\right ) \left (c_{2} \ln \left (x \right )+c_{1} \right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 42

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

\[ y(x)\to c_1 \left (x^5+x^4+x^3+x^2+x+1\right )+c_2 \left (x^5+x^4+x^3+x^2+x+1\right ) \log (x) \]