Internal problem ID [14887]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {3 x y^{\prime \prime }+11 y^{\prime }-y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.062 (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);
\[ y \left (x \right ) = \frac {c_{1} \left (1-\frac {1}{5} x +\frac {1}{20} x^{2}+\frac {1}{60} x^{3}+\frac {1}{960} x^{4}+\frac {1}{33600} x^{5}+\operatorname {O}\left (x^{6}\right )\right )}{x^{\frac {8}{3}}}+c_{2} \left (1+\frac {1}{11} x +\frac {1}{308} x^{2}+\frac {1}{15708} x^{3}+\frac {1}{1256640} x^{4}+\frac {1}{144513600} x^{5}+\operatorname {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 85
AsymptoticDSolveValue[3*x*y''[x]+11*y'[x]-y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {x^5}{144513600}+\frac {x^4}{1256640}+\frac {x^3}{15708}+\frac {x^2}{308}+\frac {x}{11}+1\right )+\frac {c_2 \left (\frac {x^5}{33600}+\frac {x^4}{960}+\frac {x^3}{60}+\frac {x^2}{20}-\frac {x}{5}+1\right )}{x^{8/3}} \]