54.3.272 problem 1288

Internal problem ID [12567]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1288
Date solved : Wednesday, October 01, 2025 at 02:06:49 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 16 x^{2} y^{\prime \prime }+\left (4 x +3\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 21

ode:=16*x^2*diff(diff(y(x),x),x)+(4*x+3)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x^{{1}/{4}} \left (c_1 \sin \left (\sqrt {x}\right )+c_2 \cos \left (\sqrt {x}\right )\right ) \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 43

ode=(3 + 4*x)*y[x] + 16*x^2*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-i \sqrt {x}} \sqrt [4]{x} \left (c_1 e^{2 i \sqrt {x}}+i c_2\right ) \end{align*}

✓ Sympy. Time used: 0.046 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(16*x**2*Derivative(y(x), (x, 2)) + (4*x + 3)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \sqrt {x} \left (C_{1} J_{\frac {1}{2}}\left (\sqrt {x}\right ) + C_{2} Y_{\frac {1}{2}}\left (\sqrt {x}\right )\right ) \]