60.3.330 problem 1336

Internal problem ID [11340]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1336
Date solved : Monday, January 27, 2025 at 11:15:33 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }&=-\frac {\left (-3 x +1\right ) y}{\left (x -1\right ) \left (2 x -1\right )^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 44

dsolve(diff(diff(y(x),x),x) = -(-3*x+1)/(x-1)/(2*x-1)^2*y(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.138 (sec). Leaf size: 70

DSolve[D[y[x],{x,2}] == -(((1 - 3*x)*y[x])/((-1 + x)*(-1 + 2*x)^2)),y[x],x,IncludeSingularSolutions -> True]
 

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