74.18.62 problem 68

Internal problem ID [16619]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number : 68
Date solved : Tuesday, January 28, 2025 at 09:12:56 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.070 (sec). Leaf size: 33

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

\[ y = c_{1} x^{7} \left (1+\frac {1}{8} x^{2}+\frac {1}{160} x^{4}+\operatorname {O}\left (x^{6}\right )\right )+c_{2} x \left (-86400+21600 x^{2}-5400 x^{4}+\operatorname {O}\left (x^{6}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 44

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

\[ y(x)\to c_1 \left (\frac {x^5}{16}-\frac {x^3}{4}+x\right )+c_2 \left (\frac {x^{11}}{160}+\frac {x^9}{8}+x^7\right ) \]