34.5.3 problem 8

Internal problem ID [6071]
Book : A treatise on ordinary and partial differential equations by William Woolsey Johnson. 1913
Section : Chapter VII, Solutions in series. Examples XVI. page 220
Problem number : 8
Date solved : Monday, January 27, 2025 at 01:34:52 PM
CAS classification : [_Jacobi]

\begin{align*} 2 x \left (1-x \right ) y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 44

Order:=6; 
dsolve(2*x*(1-x)*diff(y(x),x$2)+(1-11*x)*diff(y(x),x)-10*y(x)=0,y(x),type='series',x=0);
 

\[ y = c_1 \sqrt {x}\, \left (1+5 x +14 x^{2}+30 x^{3}+55 x^{4}+91 x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_2 \left (1+10 x +35 x^{2}+84 x^{3}+165 x^{4}+286 x^{5}+\operatorname {O}\left (x^{6}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 65

AsymptoticDSolveValue[2*x*(1-x)*D[y[x],{x,2}]+(1-11*x)*D[y[x],x]-10*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_1 \sqrt {x} \left (91 x^5+55 x^4+30 x^3+14 x^2+5 x+1\right )+c_2 \left (286 x^5+165 x^4+84 x^3+35 x^2+10 x+1\right ) \]