60.3.384 problem 1390

Internal problem ID [11394]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1390
Date solved : Monday, January 27, 2025 at 11:19:13 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }&=-\frac {3 y}{16 x^{2} \left (x -1\right )^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 25

dsolve(diff(diff(y(x),x),x) = -3/16/x^2/(x-1)^2*y(x),y(x), singsol=all)
 

\[ y = c_{1} \left (x -1\right )^{{1}/{4}} x^{{3}/{4}}+c_{2} \left (x -1\right )^{{3}/{4}} x^{{1}/{4}} \]

✓ Solution by Mathematica

Time used: 0.182 (sec). Leaf size: 74

DSolve[D[y[x],{x,2}] == (-3*y[x])/(16*(-1 + x)^2*x^2),y[x],x,IncludeSingularSolutions -> True]
 

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