Internal problem ID [14807]
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: 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {5 x y^{\prime \prime }+8 y^{\prime }-y x=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 32
Order:=6; dsolve(5*x*diff(y(x),x$2)+8*diff(y(x),x)-x*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \frac {c_{1} \left (1+\frac {1}{14} x^{2}+\frac {1}{952} x^{4}+\operatorname {O}\left (x^{6}\right )\right )}{x^{\frac {3}{5}}}+c_{2} \left (1+\frac {1}{26} x^{2}+\frac {1}{2392} x^{4}+\operatorname {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 47
AsymptoticDSolveValue[5*x*y''[x]+8*y'[x]-x*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {x^4}{2392}+\frac {x^2}{26}+1\right )+\frac {c_2 \left (\frac {x^4}{952}+\frac {x^2}{14}+1\right )}{x^{3/5}} \]