40.16.1 problem 9

Internal problem ID [6792]
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
Date solved : Monday, January 27, 2025 at 02:30:37 PM
CAS classification : [_linear]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 32

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

\[ y = \left (1-x \right ) y \left (0\right )+\frac {x^{3}}{3}+\frac {x^{4}}{6}+\frac {x^{5}}{10}+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 33

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

\[ y(x)\to \frac {x^5}{10}+\frac {x^4}{6}+\frac {x^3}{3}+c_1 (1-x) \]