Internal problem ID [14813]
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: 12.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
\[ \boxed {y^{\prime \prime }+\left (\frac {16}{3 x}-1\right ) y^{\prime }-\frac {16 y}{3 x^{2}}=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 45
Order:=6; dsolve(diff(y(x),x$2)+(16/3*1/x-1)*diff(y(x),x)-16/3*1/x^2*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \frac {c_{1} \left (1+x +\frac {1}{2} x^{2}+\frac {1}{6} x^{3}+\frac {1}{24} x^{4}+\frac {1}{120} x^{5}+\operatorname {O}\left (x^{6}\right )\right )}{x^{\frac {16}{3}}}+c_{2} x \left (1+\frac {3}{22} x +\frac {9}{550} x^{2}+\frac {27}{15400} x^{3}+\frac {81}{477400} x^{4}+\frac {243}{16231600} x^{5}+\operatorname {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 82
AsymptoticDSolveValue[y''[x]+(16/3*1/x-1)*y'[x]-16/3*1/x^2*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 x \left (\frac {243 x^5}{16231600}+\frac {81 x^4}{477400}+\frac {27 x^3}{15400}+\frac {9 x^2}{550}+\frac {3 x}{22}+1\right )+\frac {c_2 \left (\frac {x^5}{120}+\frac {x^4}{24}+\frac {x^3}{6}+\frac {x^2}{2}+x+1\right )}{x^{16/3}} \]