Internal problem ID [2399]
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: 24.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {3 x^{2} y^{\prime \prime }+2 y^{\prime } x +\left (x^{2}-2\right ) y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
Order:=6; dsolve(3*x^2*diff(y(x),x$2)+2*x*diff(y(x),x)+(x^2-2)*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \frac {c_{2} x^{\frac {5}{3}} \left (1-\frac {1}{22} x^{2}+\frac {1}{1496} x^{4}+\operatorname {O}\left (x^{6}\right )\right )+c_{1} \left (1-\frac {1}{2} x^{2}+\frac {1}{56} x^{4}+\operatorname {O}\left (x^{6}\right )\right )}{x^{\frac {2}{3}}} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 48
AsymptoticDSolveValue[3*x^2*y''[x]+2*x*y'[x]+(x^2-2)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 x \left (\frac {x^4}{1496}-\frac {x^2}{22}+1\right )+\frac {c_2 \left (\frac {x^4}{56}-\frac {x^2}{2}+1\right )}{x^{2/3}} \]