Internal problem ID [14009]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 36. The big theorem on the the Frobenius method. Additional Exercises. page
739
Problem number: 36.2 (e).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-\left (2 x^{2}+5 x \right ) y^{\prime }+9 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 69
Order:=6; dsolve(x^2*diff(y(x),x$2)-(5*x+2*x^2)*diff(y(x),x)+9*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (\left (c_{1} +c_{2} \ln \left (x \right )\right ) \left (1+6 x +12 x^{2}+\frac {40}{3} x^{3}+10 x^{4}+\frac {28}{5} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+\left (\left (-10\right ) x -29 x^{2}-\frac {346}{9} x^{3}-\frac {193}{6} x^{4}-\frac {1459}{75} x^{5}+\operatorname {O}\left (x^{6}\right )\right ) c_{2} \right ) x^{3} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 112
AsymptoticDSolveValue[x^2*y''[x]-(5*x+2*x^2)*y'[x]+9*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {28 x^5}{5}+10 x^4+\frac {40 x^3}{3}+12 x^2+6 x+1\right ) x^3+c_2 \left (\left (-\frac {1459 x^5}{75}-\frac {193 x^4}{6}-\frac {346 x^3}{9}-29 x^2-10 x\right ) x^3+\left (\frac {28 x^5}{5}+10 x^4+\frac {40 x^3}{3}+12 x^2+6 x+1\right ) x^3 \log (x)\right ) \]