40.16.5 problem 12

Internal problem ID [6796]
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
Date solved : Monday, January 27, 2025 at 02:30:42 PM
CAS classification : [_linear]

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

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 35

Order:=6; 
dsolve((x+1)*diff(y(x),x)=x^2-2*x+y(x),y(x),type='series',x=0);
 

\[ y = \left (x +1\right ) y \left (0\right )-x^{2}+\frac {2 x^{3}}{3}-\frac {x^{4}}{3}+\frac {x^{5}}{5}+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 36

AsymptoticDSolveValue[(x+1)*D[y[x],x]==x^2-2*x+y[x],y[x],{x,0,"6"-1}]
 

\[ y(x)\to \frac {x^5}{5}-\frac {x^4}{3}+\frac {2 x^3}{3}-x^2+c_1 (x+1) \]