Internal problem ID [2394]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 41, page 195
Problem number: 19.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {4 x^{2} \left (x +1\right ) y^{\prime \prime }-5 y^{\prime } x +2 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 47
Order:=6; dsolve(4*x^2*(1+x)*diff(y(x),x$2)-5*x*diff(y(x),x)+2*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = c_{1} x^{\frac {1}{4}} \left (1-\frac {1}{4} x +\frac {5}{32} x^{2}-\frac {15}{128} x^{3}+\frac {195}{2048} x^{4}-\frac {663}{8192} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_{2} x^{2} \left (1-\frac {8}{11} x +\frac {32}{55} x^{2}-\frac {512}{1045} x^{3}+\frac {2048}{4807} x^{4}-\frac {16384}{43263} x^{5}+\operatorname {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 88
AsymptoticDSolveValue[4*x^2*(1+x)*y''[x]-5*x*y'[x]+2*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (-\frac {16384 x^5}{43263}+\frac {2048 x^4}{4807}-\frac {512 x^3}{1045}+\frac {32 x^2}{55}-\frac {8 x}{11}+1\right ) x^2+c_2 \left (-\frac {663 x^5}{8192}+\frac {195 x^4}{2048}-\frac {15 x^3}{128}+\frac {5 x^2}{32}-\frac {x}{4}+1\right ) \sqrt [4]{x} \]