60.3.318 problem 1324

Internal problem ID [11328]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1324
Date solved : Monday, January 27, 2025 at 11:13:21 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }&=\frac {\left (5 x -4\right ) y^{\prime }}{x \left (x -1\right )}-\frac {\left (9 x -6\right ) y}{x^{2} \left (x -1\right )} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 18

dsolve(diff(diff(y(x),x),x) = 1/x*(5*x-4)/(x-1)*diff(y(x),x)-(9*x-6)/x^2/(x-1)*y(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.243 (sec). Leaf size: 98

DSolve[D[y[x],{x,2}] == -(((-6 + 9*x)*y[x])/((-1 + x)*x^2)) + ((-4 + 5*x)*D[y[x],x])/((-1 + x)*x),y[x],x,IncludeSingularSolutions -> True]
 

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