Internal problem ID [2415]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 42, page 206
Problem number: 14.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (x -4\right ) y^{\prime }+4 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 61
Order:=6; dsolve(x^2*(x+1)*diff(y(x),x$2)+x*(x-4)*diff(y(x),x)+4*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (c_{1} x^{3} \left (1-4 x +10 x^{2}-20 x^{3}+35 x^{4}-56 x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_{2} \left (\ln \left (x \right ) \left (\left (-36\right ) x^{3}+144 x^{4}-360 x^{5}+\operatorname {O}\left (x^{6}\right )\right )+\left (12+6 x +12 x^{2}-240 x^{3}+852 x^{4}-2022 x^{5}+\operatorname {O}\left (x^{6}\right )\right )\right )\right ) x \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 70
AsymptoticDSolveValue[x^2*(x+1)*y''[x]+x*(x-4)*y'[x]+4*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (3 (4 x-1) x^4 \log (x)+\frac {1}{2} \left (62 x^4-20 x^3+2 x^2+x+2\right ) x\right )+c_2 \left (35 x^8-20 x^7+10 x^6-4 x^5+x^4\right ) \]