60.3.325 problem 1331

Internal problem ID [11335]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1331
Date solved : Monday, January 27, 2025 at 11:15:26 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }&=\frac {\left (x -4\right ) y^{\prime }}{2 x \left (x -2\right )}-\frac {\left (x -3\right ) y}{2 x^{2} \left (x -2\right )} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 19

dsolve(diff(diff(y(x),x),x) = 1/2/x*(x-4)/(x-2)*diff(y(x),x)-1/2*(x-3)/x^2/(x-2)*y(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.297 (sec). Leaf size: 57

DSolve[D[y[x],{x,2}] == -1/2*((-3 + x)*y[x])/((-2 + x)*x^2) + ((-4 + x)*D[y[x],x])/(2*(-2 + x)*x),y[x],x,IncludeSingularSolutions -> True]
 

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