34.3.6 problem 7

Internal problem ID [6045]
Book : A treatise on ordinary and partial differential equations by William Woolsey Johnson. 1913
Section : Chapter VII, Solutions in series. Examples XIV. page 177
Problem number : 7
Date solved : Monday, January 27, 2025 at 01:34:21 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using series method with expansion around

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

✗ Solution by Maple

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

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 49

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

\[ y(x)\to \frac {c_1 \left (1-x^2\right )}{x}+c_2 e^{\frac {1}{2 x^2}} \left (420 x^6+45 x^4+6 x^2+1\right ) x^4 \]