12.14.50 problem 61

Internal problem ID [1991]
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 : 61
Date solved : Monday, January 27, 2025 at 05:39:50 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+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: 40

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

\[ y = \left (-x^{5}+x^{4}-x^{3}+x^{2}-x +1\right ) \left (c_1 \sqrt {x}+c_2 x \right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 58

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

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