59.1.269 problem 272

Internal problem ID [9441]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 272
Date solved : Monday, January 27, 2025 at 06:02:52 PM
CAS classification : [_Jacobi]

\begin{align*} 2 x \left (1-x \right ) y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.024 (sec). Leaf size: 29

dsolve(2*x*(1-x)*diff(y(x),x$2)+(1-11*x)*diff(y(x),x)-10*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{1} \left (x^{2}+6 x +1\right )+c_{2} \sqrt {x}\, \left (x +1\right )}{\left (x -1\right )^{4}} \]

✓ Solution by Mathematica

Time used: 0.548 (sec). Leaf size: 119

DSolve[2*x*(1-x)*D[y[x],{x,2}]+(1-11*x)*D[y[x],x]-10*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to (x+1) \exp \left (\int _1^x\frac {3 K[1]+3}{4 K[1]-4 K[1]^2}dK[1]-\frac {1}{2} \int _1^x\left (\frac {1}{2 K[2]}+\frac {5}{K[2]-1}\right )dK[2]\right ) \left (c_2 \int _1^x\frac {\exp \left (-2 \int _1^{K[3]}\frac {3 K[1]+3}{4 K[1]-4 K[1]^2}dK[1]\right )}{(K[3]+1)^2}dK[3]+c_1\right ) \]