54.3.273 problem 1289

Internal problem ID [12568]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1289
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 }+32 x y^{\prime }-\left (4 x +5\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.052 (sec). Leaf size: 33

ode:=16*x^2*diff(diff(y(x),x),x)+32*x*diff(y(x),x)-(4*x+5)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{\sqrt {x}} c_1 \left (-1+\sqrt {x}\right )+{\mathrm e}^{-\sqrt {x}} c_2 \left (\sqrt {x}+1\right )}{x^{{5}/{4}}} \]

✓ Mathematica. Time used: 0.603 (sec). Leaf size: 65

ode=(-5 - 4*x)*y[x] + 32*x*D[y[x],x] + 16*x^2*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {e^{\sqrt {x}} \left (\sqrt {x}-1\right ) \left (c_2 \int _1^x\frac {e^{-2 \sqrt {K[1]}} \sqrt {K[1]}}{\left (\sqrt {K[1]}-1\right )^2}dK[1]+c_1\right )}{x^{5/4}} \end{align*}

✓ Sympy. Time used: 0.140 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(16*x**2*Derivative(y(x), (x, 2)) + 32*x*Derivative(y(x), x) - (4*x + 5)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} J_{\frac {3}{2}}\left (i \sqrt {x}\right ) + C_{2} Y_{\frac {3}{2}}\left (i \sqrt {x}\right )}{\sqrt {x}} \]