52.2.9 problem 9

Internal problem ID [8260]
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 : 9
Date solved : Monday, January 27, 2025 at 03:47:18 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{3} \left (x^{2}-25\right ) \left (x -2\right )^{2} y^{\prime \prime }+3 x \left (x -2\right ) y^{\prime }+7 \left (5+x \right ) y&=0 \end{align*}

Using series method with expansion around

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

✗ Solution by Maple

Order:=8; 
dsolve(x^3*(x^2-25)*(x-2)^2*diff(y(x),x$2)+3*x*(x-2)*diff(y(x),x)+7*(x+5)*y(x)=0,y(x),type='series',x=0);
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.177 (sec). Leaf size: 127

AsymptoticDSolveValue[x^3*(x^2-25)*(x-2)^2*D[y[x],{x,2}]+3*x*(x-2)*D[y[x],x]+7*(x+5)*y[x]==0,y[x],{x,0,"8"-1}]
 

\[ y(x)\to c_2 \left (-\frac {8443721376476278698619699192242145 x^7}{24679069470425088}+\frac {256276439033972389997207276999 x^6}{228509902503936}-\frac {1337698720169782190618881 x^5}{352638738432}+\frac {42840301537653264505 x^4}{3265173504}-\frac {344729362309955 x^3}{7558272}+\frac {3590248795 x^2}{23328}-\frac {50309 x}{108}+1\right ) x^{35/6}+\frac {c_1 e^{\left .\frac {3}{50}\right /x} \left (\frac {27670480145177700385838149741665715823829792301 x^7}{4118764073681250000000000000000000000000}+\frac {3104172516869718247583976968553108060901 x^6}{4358480501250000000000000000000000}-\frac {37907198008560463448473952765642999 x^5}{5380840125000000000000000000}+\frac {27497874350326089989823180601 x^4}{7971615000000000000000}+\frac {10649898771731482781701 x^3}{14762250000000000}+\frac {975156065160301 x^2}{36450000000}+\frac {41066401 x}{135000}+1\right )}{x^{1159/300}} \]