Internal problem ID [2416]
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: 15.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+x \left (-x^{2}+3\right ) y^{\prime }-3 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 47
Order:=6; dsolve(x^2*diff(y(x),x$2)+x*(3-x^2)*diff(y(x),x)-3*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \frac {c_{1} x^{4} \left (1+\frac {1}{12} x^{2}+\frac {1}{128} x^{4}+\operatorname {O}\left (x^{6}\right )\right )+c_{2} \left (\ln \left (x \right ) \left (27 x^{4}+\operatorname {O}\left (x^{6}\right )\right )+\left (-144-108 x^{2}-36 x^{4}+\operatorname {O}\left (x^{6}\right )\right )\right )}{x^{3}} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 53
AsymptoticDSolveValue[x^2*y''[x]+x*(3-x^2)*y'[x]-3*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {x^5}{128}+\frac {x^3}{12}+x\right )+c_1 \left (\frac {19 x^4+48 x^2+64}{64 x^3}-\frac {3}{16} x \log (x)\right ) \]