Internal problem ID [2393]
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: 18.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {2 x^{2} \left (1-3 x \right ) y^{\prime \prime }+5 y^{\prime } x -2 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 41
Order:=6; dsolve(2*x^2*(1-3*x)*diff(y(x),x$2)+5*x*diff(y(x),x)-2*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \frac {c_{2} x^{\frac {5}{2}} \left (1-\frac {3}{14} x -\frac {3}{56} x^{2}-\frac {45}{1232} x^{3}-\frac {675}{18304} x^{4}-\frac {1701}{36608} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_{1} \left (1-12 x +72 x^{2}+\operatorname {O}\left (x^{6}\right )\right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 63
AsymptoticDSolveValue[2*x^2*(1-3*x)*y''[x]+5*x*y'[x]-2*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to \frac {c_2 \left (72 x^2-12 x+1\right )}{x^2}+c_1 \sqrt {x} \left (-\frac {1701 x^5}{36608}-\frac {675 x^4}{18304}-\frac {45 x^3}{1232}-\frac {3 x^2}{56}-\frac {3 x}{14}+1\right ) \]