56.4.59 problem 56

Internal problem ID [8948]
Book : Own collection of miscellaneous problems
Section : section 4.0
Problem number : 56
Date solved : Monday, January 27, 2025 at 05:20:38 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 32

Order:=6; 
dsolve(2*x^2*diff(y(x),x$2)+5*x*diff(y(x),x)+4*y(x) = 0,y(x),type='series',x=0);
 

\[ y = \frac {x^{-\frac {i \sqrt {23}}{4}} c_{1} +x^{\frac {i \sqrt {23}}{4}} c_{2}}{x^{{3}/{4}}}+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 44

AsymptoticDSolveValue[2*x^2*D[y[x],{x,2}]+5*x*D[y[x],x]+4*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_1 x^{\frac {1}{4} \left (-3+i \sqrt {23}\right )}+c_2 x^{\frac {1}{4} \left (-3-i \sqrt {23}\right )} \]