Internal problem ID [15484]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 18.2. Expanding a solution in generalized power
series. Bessels equation. Exercises page 177
Problem number: 740.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (x +1\right ) y^{\prime }-n y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 114
Order:=6; dsolve((1+x)*diff(y(x),x)-n*y(x)=0,y(x),type='series',x=0);
\[ y = \left (1+n x +\frac {n \left (-1+n \right ) x^{2}}{2}+\frac {n \left (n^{2}-3 n +2\right ) x^{3}}{6}+\frac {n \left (n^{3}-6 n^{2}+11 n -6\right ) x^{4}}{24}+\frac {n \left (n^{4}-10 n^{3}+35 n^{2}-50 n +24\right ) x^{5}}{120}\right ) y \left (0\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 143
AsymptoticDSolveValue[(1+x)*y'[x]-n*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {n^5 x^5}{120}-\frac {n^4 x^5}{12}+\frac {n^4 x^4}{24}+\frac {7 n^3 x^5}{24}-\frac {n^3 x^4}{4}+\frac {n^3 x^3}{6}-\frac {5 n^2 x^5}{12}+\frac {11 n^2 x^4}{24}-\frac {n^2 x^3}{2}+\frac {n^2 x^2}{2}+\frac {n x^5}{5}-\frac {n x^4}{4}+\frac {n x^3}{3}-\frac {n x^2}{2}+n x+1\right ) \]