74.18.61 problem 67

Internal problem ID [16618]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number : 67
Date solved : Tuesday, January 28, 2025 at 09:12:55 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }-2 y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.051 (sec). Leaf size: 20

Order:=6; 
dsolve(2*x^2*diff(y(x),x$2)+5*x*diff(y(x),x)-2*y(x)=0,y(x),type='series',x=0);
 

\[ y = \frac {x^{{5}/{2}} c_{2} +c_{1}}{x^{2}}+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

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

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

\[ y(x)\to \frac {c_2}{x^2}+c_1 \sqrt {x} \]