56.4.51 problem 48

Internal problem ID [8940]
Book : Own collection of miscellaneous problems
Section : section 4.0
Problem number : 48
Date solved : Monday, January 27, 2025 at 05:20:27 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 34

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

\[ y = c_{1} x \left (1+\operatorname {O}\left (x^{6}\right )\right )+\left (x +\operatorname {O}\left (x^{6}\right )\right ) \ln \left (x \right ) c_{2} +\left (1-x +\operatorname {O}\left (x^{6}\right )\right ) c_{2} \]

✓ Solution by Mathematica

Time used: 0.049 (sec). Leaf size: 20

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

\[ y(x)\to c_2 x+c_1 (-3 x+x \log (x)+1) \]