Internal problem ID [14803]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.9, page 215
Problem number: 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x \left (x +1\right ) y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}+5 y=0} \] With the expansion point for the power series method at \(x = 0\).
✗ Solution by Maple
Order:=6; dsolve(x*(x+1)*diff(y(x),x$2)+diff(y(x),x)/x^2+5*y(x)=0,y(x),type='series',x=0);
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.055 (sec). Leaf size: 73
AsymptoticDSolveValue[x*(1+x)*y''[x]+y'[x]/x^2+5*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (2 x^5-\frac {5 x^3}{3}+1\right )+c_2 e^{\frac {1}{2 x^2}-\frac {1}{x}} \left (\frac {272 x^5}{3}+\frac {88 x^4}{3}+\frac {35 x^3}{3}+4 x^2+2 x+1\right ) x^2 \]