12.14.52 problem 63

Internal problem ID [1993]
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 : 63
Date solved : Monday, January 27, 2025 at 05:39:53 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 28 x^{2} \left (1-3 x \right ) y^{\prime \prime }-7 x \left (5+9 x \right ) y^{\prime }+7 \left (2+9 x \right ) y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 46

Order:=6; 
dsolve(28*x^2*(1-3*x)*diff(y(x),x$2)-7*x*(5+9*x)*diff(y(x),x)+7*(2+9*x)*y(x)=0,y(x),type='series',x=0);
 

\[ y = \left (243 x^{5}+81 x^{4}+27 x^{3}+9 x^{2}+3 x +1\right ) \left (c_1 \,x^{{1}/{4}}+c_2 \,x^{2}\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 68

AsymptoticDSolveValue[28*x^2*(1-3*x)*D[y[x],{x,2}]-7*x*(5+9*x)*D[y[x],x]+7*(2+9*x)*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_1 \left (243 x^5+81 x^4+27 x^3+9 x^2+3 x+1\right ) x^2+c_2 \left (243 x^5+81 x^4+27 x^3+9 x^2+3 x+1\right ) \sqrt [4]{x} \]