Internal problem ID [14806]
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: 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {2 x y^{\prime \prime }-5 y^{\prime }-3 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 44
Order:=6; dsolve(2*x*diff(y(x),x$2)-5*diff(y(x),x)-3*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = c_{1} x^{\frac {7}{2}} \left (1+\frac {1}{3} x +\frac {1}{22} x^{2}+\frac {1}{286} x^{3}+\frac {1}{5720} x^{4}+\frac {3}{486200} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_{2} \left (1-\frac {3}{5} x +\frac {3}{10} x^{2}-\frac {3}{10} x^{3}-\frac {9}{40} x^{4}-\frac {9}{200} x^{5}+\operatorname {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 85
AsymptoticDSolveValue[2*x*y''[x]-5*y'[x]-3*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (-\frac {9 x^5}{200}-\frac {9 x^4}{40}-\frac {3 x^3}{10}+\frac {3 x^2}{10}-\frac {3 x}{5}+1\right )+c_1 \left (\frac {3 x^5}{486200}+\frac {x^4}{5720}+\frac {x^3}{286}+\frac {x^2}{22}+\frac {x}{3}+1\right ) x^{7/2} \]