12.14.51 problem 62

Internal problem ID [1992]
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 : 62
Date solved : Monday, January 27, 2025 at 05:39:52 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 6 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (50 x^{2}+1\right ) y^{\prime }+\left (30 x^{2}+1\right ) y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 32

Order:=6; 
dsolve(6*x^2*(1+2*x^2)*diff(y(x),x$2)+x*(1+50*x^2)*diff(y(x),x)+(1+30*x^2)*y(x)=0,y(x),type='series',x=0);
 

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

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 44

AsymptoticDSolveValue[6*x^2*(1+2*x^2)*D[y[x],{x,2}]+x*(1+50*x^2)*D[y[x],x]+(1+30*x^2)*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_1 \sqrt {x} \left (4 x^4-2 x^2+1\right )+c_2 \sqrt [3]{x} \left (4 x^4-2 x^2+1\right ) \]