52.2.31 problem 31

Internal problem ID [8282]
Book : DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL, WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th edition.
Section : CHAPTER 6 SERIES SOLUTIONS OF LINEAR EQUATIONS. 6.3 SOLUTIONS ABOUT SINGULAR POINTS. EXERCISES 6.3. Page 255
Problem number : 31
Date solved : Monday, January 27, 2025 at 03:47:49 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x y^{\prime \prime }+\left (x -6\right ) y^{\prime }-3 y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 46

Order:=8; 
dsolve(x*diff(y(x),x$2)+(x-6)*diff(y(x),x)-3*y(x)=0,y(x),type='series',x=0);
 

\[ y = c_{1} x^{7} \left (1-\frac {1}{2} x +\frac {5}{36} x^{2}-\frac {1}{36} x^{3}+\frac {7}{1584} x^{4}-\frac {7}{11880} x^{5}+\frac {7}{102960} x^{6}-\frac {1}{144144} x^{7}+\operatorname {O}\left (x^{8}\right )\right )+c_{2} \left (3628800-1814400 x +362880 x^{2}-30240 x^{3}+36 x^{7}+\operatorname {O}\left (x^{8}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.105 (sec). Leaf size: 77

AsymptoticDSolveValue[x*D[y[x],{x,2}]+(x-6)*D[y[x],x]-3*y[x]==0,y[x],{x,0,"8"-1}]
 

\[ y(x)\to c_1 \left (-\frac {x^3}{120}+\frac {x^2}{10}-\frac {x}{2}+1\right )+c_2 \left (\frac {7 x^{13}}{102960}-\frac {7 x^{12}}{11880}+\frac {7 x^{11}}{1584}-\frac {x^{10}}{36}+\frac {5 x^9}{36}-\frac {x^8}{2}+x^7\right ) \]