12.16.4 problem Example 7.7.4 page 387

Internal problem ID [2066]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 7 Series Solutions of Linear Second Equations. 7.6 THE METHOD OF FROBENIUS III. Exercises 7.7. Page 389
Problem number : Example 7.7.4 page 387
Date solved : Monday, January 27, 2025 at 05:41:27 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-13 x^{2}+7\right ) y^{\prime }-14 x^{2} y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 32

Order:=6; 
dsolve(x^2*(1-2*x^2)*diff(y(x),x$2)+x*(7-13*x^2)*diff(y(x),x)-14*x^2*y(x)=0,y(x),type='series',x=0);
 

\[ y = c_1 \left (1+\frac {7}{8} x^{2}+\frac {77}{80} x^{4}+\operatorname {O}\left (x^{6}\right )\right )+\frac {c_2 \left (-86400+216000 x^{2}-54000 x^{4}+\operatorname {O}\left (x^{6}\right )\right )}{x^{6}} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 44

AsymptoticDSolveValue[x^2*(1-2*x^2)*D[y[x],{x,2}]+x*(7-13*x^2)*D[y[x],x]-14*x^2*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_2 \left (\frac {77 x^4}{80}+\frac {7 x^2}{8}+1\right )+c_1 \left (\frac {1}{x^6}-\frac {5}{2 x^4}+\frac {5}{8 x^2}\right ) \]