75.24.2 problem 740

Internal problem ID [17214]
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 ODEs). Section 18.2. Expanding a solution in generalized power series. Bessels equation. Exercises page 177
Problem number : 740
Date solved : Tuesday, January 28, 2025 at 09:57:45 AM
CAS classification : [_separable]

\begin{align*} \left (1+x \right ) y^{\prime }-n y&=0 \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 83

Order:=6; 
dsolve((1+x)*diff(y(x),x)-n*y(x)=0,y(x),type='series',x=0);
 

\[ y = \left (1+n x +\frac {n \left (n -1\right ) x^{2}}{2}+\frac {n \left (n^{2}-3 n +2\right ) x^{3}}{6}+\frac {n \left (n^{3}-6 n^{2}+11 n -6\right ) x^{4}}{24}+\frac {n \left (n^{4}-10 n^{3}+35 n^{2}-50 n +24\right ) x^{5}}{120}\right ) y \left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 143

AsymptoticDSolveValue[(1+x)*D[y[x],x]-n*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_1 \left (\frac {n^5 x^5}{120}-\frac {n^4 x^5}{12}+\frac {n^4 x^4}{24}+\frac {7 n^3 x^5}{24}-\frac {n^3 x^4}{4}+\frac {n^3 x^3}{6}-\frac {5 n^2 x^5}{12}+\frac {11 n^2 x^4}{24}-\frac {n^2 x^3}{2}+\frac {n^2 x^2}{2}+\frac {n x^5}{5}-\frac {n x^4}{4}+\frac {n x^3}{3}-\frac {n x^2}{2}+n x+1\right ) \]