60.3.373 problem 1390

Internal problem ID [11369]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1390
Date solved : Sunday, March 30, 2025 at 08:18:35 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*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 25

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

\[ y = c_1 \,x^{{3}/{4}} \left (x -1\right )^{{1}/{4}}+c_2 \,x^{{1}/{4}} \left (x -1\right )^{{3}/{4}} \]

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

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

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

✓ Sympy. Time used: 0.248 (sec). Leaf size: 34

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), (x, 2)) + 3*y(x)/(16*x**2*(x - 1)**2),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \sqrt [4]{x} \sqrt [4]{x - 1} \left (C_{1} \sqrt {x} {{}_{2}F_{1}\left (\begin {matrix} 0, 1 \\ \frac {3}{2} \end {matrix}\middle | {x} \right )} + C_{2} {{}_{1}F_{0}\left (\begin {matrix} - \frac {1}{2} \\ \end {matrix}\middle | {x} \right )}\right ) \]