Internal problem ID [8872]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1292.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Jacobi, [_2nd_order, _linear, _with_symmetry_[0,F(x)]]]
Solve \begin {gather*} \boxed {50 x \left (x -1\right ) y^{\prime \prime }+25 \left (2 x -1\right ) y^{\prime }-2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 31
dsolve(50*x*(x-1)*diff(diff(y(x),x),x)+25*(2*x-1)*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (\sqrt {x}+\sqrt {x -1}\right )^{\frac {2}{5}}+\frac {c_{2}}{\left (\sqrt {x}+\sqrt {x -1}\right )^{\frac {2}{5}}} \]
✓ Solution by Mathematica
Time used: 0.045 (sec). Leaf size: 49
DSolve[-2*y[x] + 25*(-1 + 2*x)*y'[x] + 50*(-1 + x)*x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \cosh \left (\frac {2}{5} \tanh ^{-1}\left (\frac {1}{\sqrt {\frac {x-1}{x}}}\right )\right )+i c_2 \sinh \left (\frac {2}{5} \tanh ^{-1}\left (\frac {1}{\sqrt {\frac {x-1}{x}}}\right )\right ) \\ \end{align*}