12.14.25 problem 25

Internal problem ID [1966]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 7 Series Solutions of Linear Second Equations. 7.5 THE METHOD OF FROBENIUS I. Exercises 7.5. Page 358
Problem number : 25
Date solved : Monday, January 27, 2025 at 05:39:19 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 6 x^{2} y^{\prime \prime }+x \left (10-x \right ) y^{\prime }-\left (x +2\right ) y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 38

Order:=6; 
dsolve(6*x^2*diff(y(x),x$2)+x*(10-x)*diff(y(x),x)-(2+x)*y(x)=0,y(x),type='series',x=0);
 

\[ y = \frac {c_2 \,x^{{4}/{3}} \left (1+\frac {2}{21} x +\frac {1}{180} x^{2}+\frac {1}{4212} x^{3}+\frac {1}{124416} x^{4}+\frac {1}{4432320} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_1 \left (1+\operatorname {O}\left (x^{6}\right )\right )}{x} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 53

AsymptoticDSolveValue[6*x^2*D[y[x],{x,2}]+x*(10-x)*D[y[x],x]-(2+x)*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_1 \sqrt [3]{x} \left (\frac {x^5}{4432320}+\frac {x^4}{124416}+\frac {x^3}{4212}+\frac {x^2}{180}+\frac {2 x}{21}+1\right )+\frac {c_2}{x} \]