Internal problem ID [13693]
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 (i).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime } x +4 y^{\prime }+\frac {12 y}{\left (x +2\right )^{2}}=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 42
Order:=6; dsolve(x*diff(y(x),x$2)+4*diff(y(x),x)+12/(x+2)^2*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = c_{1} \left (1-\frac {3}{4} x +\frac {21}{40} x^{2}-\frac {27}{80} x^{3}+\frac {33}{160} x^{4}-\frac {39}{320} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+\frac {c_{2} \left (12+18 x +9 x^{2}+\frac {9}{8} x^{4}-\frac {63}{80} x^{5}+\operatorname {O}\left (x^{6}\right )\right )}{x^{3}} \]
✓ Solution by Mathematica
Time used: 0.065 (sec). Leaf size: 59
AsymptoticDSolveValue[x*y''[x]+4*y'[x]+12/(x+2)^2*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {1}{x^3}+\frac {3}{2 x^2}+\frac {3}{4 x}+\frac {1}{8}\right )+c_2 \left (\frac {33 x^4}{160}-\frac {27 x^3}{80}+\frac {21 x^2}{40}-\frac {3 x}{4}+1\right ) \]