Internal problem ID [5450]
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: 10A.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime } x -2 y=1-x} \] With the expansion point for the power series method at \(x = 1\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
Order:=6; dsolve(x*diff(y(x),x)=1-x+2*y(x),y(x),type='series',x=1);
\[ y = y \left (1\right ) x^{2}-\frac {\left (-1+x \right )^{2}}{2} \]
✓ Solution by Mathematica
Time used: 0.036 (sec). Leaf size: 28
AsymptoticDSolveValue[x*y'[x]==1-x+2*y[x],y[x],{x,1,5}]
\[ y(x)\to -\frac {1}{2} (x-1)^2+c_1 \left ((x-1)^2+2 (x-1)+1\right ) \]