74.17.7 problem 7

Internal problem ID [16538]
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 : 7
Date solved : Tuesday, January 28, 2025 at 09:10:23 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 9 x y^{\prime \prime }+14 y^{\prime }+\left (x -1\right ) y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.053 (sec). Leaf size: 44

Order:=6; 
dsolve(9*x*diff(y(x),x$2)+14*diff(y(x),x)+(x-1)*y(x)=0,y(x),type='series',x=0);
 

\[ y = \frac {c_{1} \left (1+\frac {1}{4} x -\frac {3}{104} x^{2}-\frac {29}{6864} x^{3}+\frac {13}{65472} x^{4}+\frac {251}{11348480} x^{5}+\operatorname {O}\left (x^{6}\right )\right )}{x^{{5}/{9}}}+c_{2} \left (1+\frac {1}{14} x -\frac {13}{644} x^{2}-\frac {59}{61824} x^{3}+\frac {29}{247296} x^{4}+\frac {53}{12364800} x^{5}+\operatorname {O}\left (x^{6}\right )\right ) \]

✓ Solution by Mathematica

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

AsymptoticDSolveValue[9*x*D[y[x],{x,2}]+14*D[y[x],x]+(x-1)*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_1 \left (\frac {53 x^5}{12364800}+\frac {29 x^4}{247296}-\frac {59 x^3}{61824}-\frac {13 x^2}{644}+\frac {x}{14}+1\right )+\frac {c_2 \left (\frac {251 x^5}{11348480}+\frac {13 x^4}{65472}-\frac {29 x^3}{6864}-\frac {3 x^2}{104}+\frac {x}{4}+1\right )}{x^{5/9}} \]