Internal problem ID [4220]
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: 9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Jacobi]
Solve \begin {gather*} \boxed {x \left (1-x \right ) y^{\prime \prime }+\frac {\left (1-2 x \right ) y^{\prime }}{3}+\frac {20 y}{9}=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.021 (sec). Leaf size: 36
Order:=6; dsolve(x*(1-x)*diff(y(x),x$2)+1/3*(1-2*x)*diff(y(x),x)+20/9*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{\frac {2}{3}} \left (1-\frac {6}{5} x +\mathrm {O}\left (x^{6}\right )\right )+c_{2} \left (1-\frac {20}{3} x +\frac {35}{9} x^{2}+\frac {50}{81} x^{3}+\frac {65}{243} x^{4}+\frac {112}{729} x^{5}+\mathrm {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 57
AsymptoticDSolveValue[x*(1-x)*y''[x]+1/3*(1-2*x)*y'[x]+20/9*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (1-\frac {6 x}{5}\right ) x^{2/3}+c_2 \left (\frac {112 x^5}{729}+\frac {65 x^4}{243}+\frac {50 x^3}{81}+\frac {35 x^2}{9}-\frac {20 x}{3}+1\right ) \]