59.1.303 problem 306

Internal problem ID [9475]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 306
Date solved : Monday, January 27, 2025 at 06:03:14 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} \left (1-x \right ) y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 18

dsolve((1-x)*x^2*diff(y(x),x$2)+(5*x-4)*x*diff(y(x),x)+(6-9*x)*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.247 (sec). Leaf size: 98

DSolve[(1-x)*x^2*D[y[x],{x,2}]+(5*x-4)*x*D[y[x],x]+(6-9*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \exp \left (\int _1^x\left (\frac {1}{K[1]}+\frac {1}{2-2 K[1]}\right )dK[1]-\frac {1}{2} \int _1^x\left (\frac {1}{1-K[2]}-\frac {4}{K[2]}\right )dK[2]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[3]}\frac {K[1]-2}{2 (K[1]-1) K[1]}dK[1]\right )dK[3]+c_1\right ) \]