74.17.8 problem 8

Internal problem ID [16539]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.9, page 215
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 09:10:24 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 7 x y^{\prime \prime }+10 y^{\prime }+\left (-x^{2}+1\right ) y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.054 (sec). Leaf size: 44

Order:=6; 
dsolve(7*x*diff(y(x),x$2)+10*diff(y(x),x)+(1-x^2)*y(x)=0,y(x),type='series',x=0);
 

\[ y = \frac {c_{1} \left (1-\frac {1}{4} x +\frac {1}{88} x^{2}+\frac {29}{1584} x^{3}-\frac {17}{6336} x^{4}+\frac {89}{1013760} x^{5}+\operatorname {O}\left (x^{6}\right )\right )}{x^{{3}/{7}}}+c_{2} \left (1-\frac {1}{10} x +\frac {1}{340} x^{2}+\frac {113}{8160} x^{3}-\frac {929}{1011840} x^{4}+\frac {781}{38449920} x^{5}+\operatorname {O}\left (x^{6}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 85

AsymptoticDSolveValue[7*x*D[y[x],{x,2}]+10*D[y[x],x]+(1-x^2)*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_1 \left (\frac {781 x^5}{38449920}-\frac {929 x^4}{1011840}+\frac {113 x^3}{8160}+\frac {x^2}{340}-\frac {x}{10}+1\right )+\frac {c_2 \left (\frac {89 x^5}{1013760}-\frac {17 x^4}{6336}+\frac {29 x^3}{1584}+\frac {x^2}{88}-\frac {x}{4}+1\right )}{x^{3/7}} \]