60.3.287 problem 1292

Internal problem ID [11297]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1292
Date solved : Monday, January 27, 2025 at 11:05:35 PM
CAS classification : [_Jacobi, [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} 50 x \left (x -1\right ) y^{\prime \prime }+25 \left (2 x -1\right ) y^{\prime }-2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.010 (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)
 

\[ y = \frac {c_{1} \left (\sqrt {x}+\sqrt {x -1}\right )^{{4}/{5}}+c_{2}}{\left (\sqrt {x}+\sqrt {x -1}\right )^{{2}/{5}}} \]

✓ Solution by Mathematica

Time used: 0.174 (sec). Leaf size: 49

DSolve[-2*y[x] + 25*(-1 + 2*x)*D[y[x],x] + 50*(-1 + x)*x*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \cosh \left (\frac {2}{5} \text {arctanh}\left (\frac {1}{\sqrt {\frac {x-1}{x}}}\right )\right )+i c_2 \sinh \left (\frac {2}{5} \text {arctanh}\left (\frac {1}{\sqrt {\frac {x-1}{x}}}\right )\right ) \]