60.3.332 problem 1338

Internal problem ID [11342]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1338
Date solved : Monday, January 27, 2025 at 11:15:38 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }&=\frac {\left (6 x -1\right ) y^{\prime }}{3 x \left (x -2\right )}+\frac {y}{3 x^{2} \left (x -2\right )} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 28

dsolve(diff(diff(y(x),x),x) = 1/3/x*(6*x-1)/(x-2)*diff(y(x),x)+1/3/x^2/(x-2)*y(x),y(x), singsol=all)
 

\[ y = c_{1} x \left (18 x^{2}-102 x +187\right )+c_{2} x^{{1}/{6}} \left (x -2\right )^{{17}/{6}} \]

✓ Solution by Mathematica

Time used: 0.263 (sec). Leaf size: 112

DSolve[D[y[x],{x,2}] == y[x]/(3*(-2 + x)*x^2) + ((-1 + 6*x)*D[y[x],x])/(3*(-2 + x)*x),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \exp \left (\int _1^x\frac {1-12 K[1]}{12 K[1]-6 K[1]^2}dK[1]-\frac {1}{2} \int _1^x\frac {1-6 K[2]}{3 (K[2]-2) K[2]}dK[2]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[3]}\frac {1-12 K[1]}{12 K[1]-6 K[1]^2}dK[1]\right )dK[3]+c_1\right ) \]