74.18.60 problem 66

Internal problem ID [16617]
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 : 66
Date solved : Tuesday, January 28, 2025 at 09:12:54 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 3 x y^{\prime \prime }+11 y^{\prime }-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(3*x*diff(y(x),x$2)+11*diff(y(x),x)-y(x)=0,y(x),type='series',x=0);
 

\[ y = \frac {c_{1} \left (1-\frac {1}{5} x +\frac {1}{20} x^{2}+\frac {1}{60} x^{3}+\frac {1}{960} x^{4}+\frac {1}{33600} x^{5}+\operatorname {O}\left (x^{6}\right )\right )}{x^{{8}/{3}}}+c_{2} \left (1+\frac {1}{11} x +\frac {1}{308} x^{2}+\frac {1}{15708} x^{3}+\frac {1}{1256640} x^{4}+\frac {1}{144513600} x^{5}+\operatorname {O}\left (x^{6}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 85

AsymptoticDSolveValue[3*x*D[y[x],{x,2}]+11*D[y[x],x]-y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_1 \left (\frac {x^5}{144513600}+\frac {x^4}{1256640}+\frac {x^3}{15708}+\frac {x^2}{308}+\frac {x}{11}+1\right )+\frac {c_2 \left (\frac {x^5}{33600}+\frac {x^4}{960}+\frac {x^3}{60}+\frac {x^2}{20}-\frac {x}{5}+1\right )}{x^{8/3}} \]