40.16.2 problem 10A

Internal problem ID [6793]
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
Date solved : Monday, January 27, 2025 at 02:30:38 PM
CAS classification : [_linear]

\begin{align*} x y^{\prime }&=1-x +2 y \end{align*}

Using series method with expansion around

\begin{align*} 1 \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 18

Order:=6; 
dsolve(x*diff(y(x),x)=1-x+2*y(x),y(x),type='series',x=1);
 

\[ y = y \left (1\right ) x^{2}-\frac {\left (x -1\right )^{2}}{2} \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 28

AsymptoticDSolveValue[x*D[y[x],x]==1-x+2*y[x],y[x],{x,1,"6"-1}]
 

\[ y(x)\to -\frac {1}{2} (x-1)^2+c_1 \left ((x-1)^2+2 (x-1)+1\right ) \]