Internal problem ID [14824]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.9, page 215
Problem number: 23.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Jacobi]
\[ \boxed {x \left (1-x \right ) y^{\prime \prime }+\left (-2 x +1\right ) y^{\prime }+2 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 43
Order:=6; dsolve(x*(1-x)*diff(y(x),x$2)+(1-2*x)*diff(y(x),x)+2*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (c_{1} +c_{2} \ln \left (x \right )\right ) \left (1-2 x +\operatorname {O}\left (x^{6}\right )\right )+\left (5 x -\frac {3}{2} x^{2}-\frac {2}{3} x^{3}-\frac {5}{12} x^{4}-\frac {3}{10} x^{5}+\operatorname {O}\left (x^{6}\right )\right ) c_{2} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 55
AsymptoticDSolveValue[x*(1-x)*y''[x]+(1-2*x)*y'[x]+2*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (-\frac {3 x^5}{10}-\frac {5 x^4}{12}-\frac {2 x^3}{3}-\frac {3 x^2}{2}+5 x+(1-2 x) \log (x)\right )+c_1 (1-2 x) \]