Internal problem ID [5449]
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: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {\left (1-x \right ) y^{\prime }+y=x^{2}} \] 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((1-x)*diff(y(x),x)=x^2-y(x),y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1-x \right ) y \left (0\right )+\frac {x^{3}}{3}+\frac {x^{4}}{6}+\frac {x^{5}}{10}+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 33
AsymptoticDSolveValue[(1-x)*y'[x]==x^2-y[x],y[x],{x,0,5}]
\[ y(x)\to \frac {x^5}{10}+\frac {x^4}{6}+\frac {x^3}{3}+c_1 (1-x) \]