Internal problem ID [15469]
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 18.1 Integration of differential equation in
series. Power series. Exercises page 171
Problem number: 725.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y^{\prime }-\frac {y-x}{y+x}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (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);
\[ y \left (x \right ) = 1+x -x^{2}+\frac {4}{3} x^{3}-\frac {5}{2} x^{4}+\frac {16}{3} x^{5}+\operatorname {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 32
AsymptoticDSolveValue[{y'[x]==(y[x]-x)/(y[x]+x),{y[0]==1}},y[x],{x,0,5}]
\[ y(x)\to \frac {16 x^5}{3}-\frac {5 x^4}{2}+\frac {4 x^3}{3}-x^2+x+1 \]