Internal problem ID [2388]
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: 9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {3 x^{2} y^{\prime \prime }+\left (-x^{2}+5 x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 47
Order:=6; dsolve(3*x^2*diff(y(x),x$2)+(5*x-x^2)*diff(y(x),x)+(2*x^2-1)*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \frac {c_{2} x^{\frac {4}{3}} \left (1+\frac {1}{21} x -\frac {61}{630} x^{2}-\frac {607}{73710} x^{3}+\frac {2297}{884520} x^{4}+\frac {14713}{50417640} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_{1} \left (1+x -\frac {1}{2} x^{2}-\frac {1}{6} x^{3}+\frac {1}{48} x^{4}+\frac {19}{2640} x^{5}+\operatorname {O}\left (x^{6}\right )\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 84
AsymptoticDSolveValue[3*x^2*y''[x]+(5*x-x^2)*y'[x]+(2*x^2-1)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \sqrt [3]{x} \left (\frac {14713 x^5}{50417640}+\frac {2297 x^4}{884520}-\frac {607 x^3}{73710}-\frac {61 x^2}{630}+\frac {x}{21}+1\right )+\frac {c_2 \left (\frac {19 x^5}{2640}+\frac {x^4}{48}-\frac {x^3}{6}-\frac {x^2}{2}+x+1\right )}{x} \]