10.13.22 problem 28

Internal problem ID [1382]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 5.2, Series Solutions Near an Ordinary Point, Part I. page 263
Problem number : 28
Date solved : Monday, January 27, 2025 at 04:56:27 AM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-2 y&=0 \end{align*}

Using series method with expansion around

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

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 16

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

\[ y = x +\frac {1}{6} x^{3}+\frac {1}{12} x^{4}+\frac {1}{24} x^{5}+\operatorname {O}\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 26

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

\[ y(x)\to \frac {x^5}{24}+\frac {x^4}{12}+\frac {x^3}{6}+x \]