83.27.8 problem 8

Internal problem ID [19354]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (A) at page 104
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 01:35:14 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} \left (x^{2}-x \right ) y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }-4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 58

dsolve((x^2-x)*diff(y(x),x$2)-2*(x-1)*diff(y(x),x)-4*y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = -4 c_{1} x^{3} \left (x -1\right ) \ln \left (x -1\right )+4 c_{1} x^{3} \left (x -1\right ) \ln \left (x \right )+c_{2} x^{4}+\left (-4 c_{1} -c_{2} \right ) x^{3}+2 c_{1} x^{2}+\frac {2 c_{1} x}{3}+\frac {c_{1}}{3} \]

✓ Solution by Mathematica

Time used: 0.060 (sec). Leaf size: 61

DSolve[(x^2-x)*D[y[x],{x,2}]-2*(x-1)*D[y[x],x]-4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{3} c_2 \left (12 x^3+12 (x-1) x^3 \log (1-x)-12 (x-1) x^3 \log (x)-6 x^2-2 x-1\right )-c_1 (x-1) x^3 \]