74.17.2 problem 2

Internal problem ID [16533]
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
Date solved : Tuesday, January 28, 2025 at 09:10:19 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x \left (1+x \right ) y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}+5 y&=0 \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

✗ 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: 0.063 (sec). Leaf size: 73

AsymptoticDSolveValue[x*(1+x)*D[y[x],{x,2}]+D[y[x],x]/x^2+5*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_1 \left (2 x^5-\frac {5 x^3}{3}+1\right )+c_2 e^{\frac {1}{2 x^2}-\frac {1}{x}} \left (\frac {272 x^5}{3}+\frac {88 x^4}{3}+\frac {35 x^3}{3}+4 x^2+2 x+1\right ) x^2 \]