Internal problem ID [7837]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 352.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Jacobi]
\[ \boxed {x \left (1-x \right ) y^{\prime \prime }+\left (2 x +\frac {1}{2}\right ) y^{\prime }-2 y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 61
dsolve(x*(1-x)*diff(y(x),x$2)+(1/2+2*x)*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \left (1+4 x \right )+c_{2} \left (4 \sqrt {x \left (x -1\right )}\, x -12 \ln \left (x -\frac {1}{2}+\sqrt {x \left (x -1\right )}\right ) x +26 \sqrt {x \left (x -1\right )}-3 \ln \left (x -\frac {1}{2}+\sqrt {x \left (x -1\right )}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.416 (sec). Leaf size: 64
DSolve[x*(1-x)*y''[x]+(1/2+2*x)*y'[x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} c_2 \left (\sqrt {-((x-1) x)} (2 x+13)-6 (4 x+1) \arctan \left (\frac {\sqrt {1-x}}{\sqrt {x}+1}\right )\right )+c_1 \left (x+\frac {1}{4}\right ) \]