81.6.11 problem 11

Internal problem ID [18694]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter V. Homogeneous linear differential equations. Exact equations. Exercises at page 69
Problem number : 11
Date solved : Tuesday, January 28, 2025 at 12:10:37 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} \left (x^{2}-x \right ) y^{\prime \prime }+\left (3 x -2\right ) y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 16

dsolve((x^2-x)*diff(y(x),x$2)+(3*x-2)*diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {c_{1} \ln \left (x -1\right )+c_{2}}{x} \]

✓ Solution by Mathematica

Time used: 0.053 (sec). Leaf size: 35

DSolve[(x^2-x)*D[y[x],{x,2}]+(3*x-2)*D[y[x],x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\sqrt {x-1} (c_2 \log (x-1)+c_1)}{\sqrt {1-x} x} \]