74.17.17 problem 17

Internal problem ID [16548]
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 : 17
Date solved : Tuesday, January 28, 2025 at 09:10:36 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.049 (sec). Leaf size: 19

Order:=6; 
dsolve(x^2*diff(y(x),x$2)-3*x*diff(y(x),x)+4*y(x)=0,y(x),type='series',x=0);
 

\[ y = x^{2} \left (\ln \left (x \right ) c_{2} +c_{1} \right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 18

AsymptoticDSolveValue[x^2*D[y[x],{x,2}]-3*x*D[y[x],x]+4*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_1 x^2+c_2 x^2 \log (x) \]