Internal problem ID [11054]
Book: Differential Equations, Linear, Nonlinear, Ordinary, Partial. A.C. King, J.Billingham, S.R.Otto.
Cambridge Univ. Press 2003
Section: Chapter 1 VARIABLE COEFFICIENT, SECOND ORDER DIFFERENTIAL EQUATIONS.
Problems page 28
Problem number: Problem 1.7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Jacobi]
\[ \boxed {x \left (1-x \right ) y^{\prime \prime }+\left (1-5 x \right ) y^{\prime }-4 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 59
Order:=6; dsolve(x*(1-x)*diff(y(x),x$2)+(1-5*x)*diff(y(x),x)-4*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (c_{2} \ln \left (x \right )+c_{1} \right ) \left (1+4 x +9 x^{2}+16 x^{3}+25 x^{4}+36 x^{5}+\operatorname {O}\left (x^{6}\right )\right )+\left (\left (-4\right ) x -12 x^{2}-24 x^{3}-40 x^{4}-60 x^{5}+\operatorname {O}\left (x^{6}\right )\right ) c_{2} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 87
AsymptoticDSolveValue[x*(1-x)*y''[x]+(1-5*x)*y'[x]-4*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (36 x^5+25 x^4+16 x^3+9 x^2+4 x+1\right )+c_2 \left (-60 x^5-40 x^4-24 x^3-12 x^2+\left (36 x^5+25 x^4+16 x^3+9 x^2+4 x+1\right ) \log (x)-4 x\right ) \]