Internal problem ID [2414]
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: 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+x \left (x -7\right ) y^{\prime }+\left (x +12\right ) y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 63
Order:=6; dsolve(x^2*diff(y(x),x$2)+x*(x-7)*diff(y(x),x)+(x+12)*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (c_{1} x^{4} \left (1-\frac {7}{5} x +\frac {14}{15} x^{2}-\frac {2}{5} x^{3}+\frac {1}{8} x^{4}-\frac {11}{360} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_{2} \left (\ln \left (x \right ) \left (360 x^{4}-504 x^{5}+\operatorname {O}\left (x^{6}\right )\right )+\left (-144-144 x -144 x^{2}-240 x^{3}+342 x^{4}+54 x^{5}+\operatorname {O}\left (x^{6}\right )\right )\right )\right ) x^{2} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 79
AsymptoticDSolveValue[x^2*y''[x]+x*(x-7)*y'[x]+(x+12)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (-\frac {5}{2} x^6 \log (x)-\frac {1}{12} \left (21 x^4-20 x^3-12 x^2-12 x-12\right ) x^2\right )+c_2 \left (\frac {x^{10}}{8}-\frac {2 x^9}{5}+\frac {14 x^8}{15}-\frac {7 x^7}{5}+x^6\right ) \]