75.23.2 problem 725

Internal problem ID [17199]
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 18.1 Integration of differential equation in series. Power series. Exercises page 171
Problem number : 725
Date solved : Tuesday, January 28, 2025 at 09:56:56 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {y-x}{x +y} \end{align*}

Using series method with expansion around

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 20

Order:=6; 
dsolve([diff(y(x),x)=(y(x)-x)/(y(x)+x),y(0) = 1],y(x),type='series',x=0);
 

\[ y = 1+x -x^{2}+\frac {4}{3} x^{3}-\frac {5}{2} x^{4}+\frac {16}{3} x^{5}+\operatorname {O}\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 32

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

\[ y(x)\to \frac {16 x^5}{3}-\frac {5 x^4}{2}+\frac {4 x^3}{3}-x^2+x+1 \]