40.17.1 problem 11

Internal problem ID [6802]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 26. Integration in series (singular points). Supplemetary problems. Page 218
Problem number : 11
Date solved : Monday, January 27, 2025 at 02:30:47 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 \left (x^{3}+x^{2}\right ) y^{\prime \prime }-\left (-3 x^{2}+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+x^3)*diff(y(x),x$2)-(x-3*x^2)*diff(y(x),x)+y(x)=0,y(x),type='series',x=0);
 

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

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 58

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

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