62.32.5 problem Ex 5

Internal problem ID [12982]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter VIII, Linear differential equations of the second order. Article 55. Summary. Page 129
Problem number : Ex 5
Date solved : Tuesday, January 28, 2025 at 04:46:16 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 13

dsolve(x*diff(y(x),x$2)-(2*x-1)*diff(y(x),x)+(x-1)*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{x} \left (\ln \left (x \right ) c_{2} +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 17

DSolve[x*D[y[x],{x,2}]-(2*x-1)*D[y[x],x]+(x-1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x (c_2 \log (x)+c_1) \]