74.17.6 problem 6

Internal problem ID [16537]
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 : 6
Date solved : Tuesday, January 28, 2025 at 09:10:22 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 5 x y^{\prime \prime }+8 y^{\prime }-y x&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.051 (sec). Leaf size: 32

Order:=6; 
dsolve(5*x*diff(y(x),x$2)+8*diff(y(x),x)-x*y(x)=0,y(x),type='series',x=0);
 

\[ y = \frac {c_{1} \left (1+\frac {1}{14} x^{2}+\frac {1}{952} x^{4}+\operatorname {O}\left (x^{6}\right )\right )}{x^{{3}/{5}}}+c_{2} \left (1+\frac {1}{26} x^{2}+\frac {1}{2392} x^{4}+\operatorname {O}\left (x^{6}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 47

AsymptoticDSolveValue[5*x*D[y[x],{x,2}]+8*D[y[x],x]-x*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_1 \left (\frac {x^4}{2392}+\frac {x^2}{26}+1\right )+\frac {c_2 \left (\frac {x^4}{952}+\frac {x^2}{14}+1\right )}{x^{3/5}} \]