Internal problem ID [5453]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 25. Integration in series. Supplemetary problems. Page 205
Problem number: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {\left (x +1\right ) y^{\prime }-y=x^{2}-2 x} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
Order:=6; dsolve((x+1)*diff(y(x),x)=x^2-2*x+y(x),y(x),type='series',x=0);
\[ y \left (x \right ) = \left (x +1\right ) y \left (0\right )-x^{2}+\frac {2 x^{3}}{3}-\frac {x^{4}}{3}+\frac {x^{5}}{5}+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 36
AsymptoticDSolveValue[(x+1)*y'[x]==x^2-2*x+y[x],y[x],{x,0,5}]
\[ y(x)\to \frac {x^5}{5}-\frac {x^4}{3}+\frac {2 x^3}{3}-x^2+c_1 (x+1) \]