Internal problem ID [2426]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 43, page 209
Problem number: 9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {9 x^{2} y^{\prime \prime }+10 x y^{\prime }+y=x -1} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 49
Order:=6; dsolve(9*x^2*diff(y(x),x$2)+10*x*diff(y(x),x)+y(x)=x-1,y(x),type='series',x=0);
\[ y \left (x \right ) = c_{1} x^{-\frac {1}{18}-\frac {i \sqrt {35}}{18}} \left (1+\operatorname {O}\left (x^{6}\right )\right )+c_{2} x^{-\frac {1}{18}+\frac {i \sqrt {35}}{18}} \left (1+\operatorname {O}\left (x^{6}\right )\right )+\left (-1+\frac {1}{11} x +\operatorname {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.294 (sec). Leaf size: 198
AsymptoticDSolveValue[9*x^2*y''[x]+10*x*y'[x]+y[x]==x-1,y[x],{x,0,5}]
\[ y(x)\to \frac {9 i \left (\left (\sqrt {35}-i\right ) x-\sqrt {35}+19 i\right ) x^{\frac {1}{18} \left (-1-i \sqrt {35}\right )+\frac {1}{18} \left (1+i \sqrt {35}\right )}}{\sqrt {35} \left (10 \sqrt {35}+8 i\right )}-\frac {9 i \left (\left (\sqrt {35}+i\right ) x-\sqrt {35}-19 i\right ) x^{\frac {1}{18} \left (1-i \sqrt {35}\right )+\frac {1}{18} \left (-1+i \sqrt {35}\right )}}{\sqrt {35} \left (10 \sqrt {35}-8 i\right )}+c_2 x^{\frac {1}{18} \left (-1+i \sqrt {35}\right )}+c_1 x^{\frac {1}{18} \left (-1-i \sqrt {35}\right )} \]