Internal problem ID [13921]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 33. Power series solutions I: Basic computational methods. Additional Exercises.
page 641
Problem number: 33.3 (k).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (x +1\right ) y^{\prime }-y x=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
Order:=6; dsolve((1+x)*diff(y(x),x)-x*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1+\frac {1}{2} x^{2}-\frac {1}{3} x^{3}+\frac {3}{8} x^{4}-\frac {11}{30} x^{5}\right ) y \left (0\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 36
AsymptoticDSolveValue[(1+x)*y'[x]-x*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (-\frac {11 x^5}{30}+\frac {3 x^4}{8}-\frac {x^3}{3}+\frac {x^2}{2}+1\right ) \]