15.23.10 problem 10

Internal problem ID [3360]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 41, page 195
Problem number : 10
Date solved : Monday, January 27, 2025 at 07:34:52 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x^{2} y^{\prime \prime }+x \left (x^{2}-4\right ) y^{\prime }+3 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: 34

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

\[ y \left (x \right ) = \sqrt {x}\, \left (x \left (1-\frac {1}{16} x^{2}+\frac {7}{2560} x^{4}+\operatorname {O}\left (x^{6}\right )\right ) c_{1} +\left (1-\frac {1}{16} x^{2}+\frac {5}{1536} x^{4}+\operatorname {O}\left (x^{6}\right )\right ) c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 58

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

\[ y(x)\to c_1 \left (\frac {5 x^{9/2}}{1536}-\frac {x^{5/2}}{16}+\sqrt {x}\right )+c_2 \left (\frac {7 x^{11/2}}{2560}-\frac {x^{7/2}}{16}+x^{3/2}\right ) \]