45.1.17 problem 29

Internal problem ID [7217]
Book : A FIRST COURSE IN DIFFERENTIAL EQUATIONS with Modeling Applications. Dennis G. Zill. 9th edition. Brooks/Cole. CA, USA.
Section : Chapter 6. SERIES SOLUTIONS OF LINEAR EQUATIONS. Exercises. 6.1.2 page 230
Problem number : 29
Date solved : Monday, January 27, 2025 at 02:48:20 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using series method with expansion around

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

With initial conditions

\begin{align*} y \left (0\right )&=-2\\ y^{\prime }\left (0\right )&=6 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 20

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

\[ y = -2+6 x -x^{2}-\frac {1}{3} x^{3}-\frac {1}{12} x^{4}-\frac {1}{60} x^{5}+\operatorname {O}\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 34

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

\[ y(x)\to -\frac {x^5}{60}-\frac {x^4}{12}-\frac {x^3}{3}-x^2+6 x-2 \]