Internal problem ID [2421]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 43, page 209
Problem number: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (1-2 x \right ) y^{\prime \prime }+4 x y^{\prime }-4 y=x^{2}-x} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 40
Order:=6; dsolve((1-2*x)*diff(y(x),x$2)+4*x*diff(y(x),x)-4*y(x)=x^2-x,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1+2 x^{2}+\frac {4}{3} x^{3}+\frac {2}{3} x^{4}+\frac {4}{15} x^{5}\right ) y \left (0\right )+D\left (y \right )\left (0\right ) x -\frac {x^{3}}{6}-\frac {x^{4}}{12}-\frac {x^{5}}{30}+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 60
AsymptoticDSolveValue[(1-2*x)*y''[x]+4*x*y'[x]-4*y[x]==x^2-x,y[x],{x,0,5}]
\[ y(x)\to -\frac {x^5}{30}-\frac {x^4}{12}-\frac {x^3}{6}+c_1 \left (\frac {4 x^5}{15}+\frac {2 x^4}{3}+\frac {4 x^3}{3}+2 x^2+1\right )+c_2 x \]