60.3.274 problem 1290

Internal problem ID [11270]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1290
Date solved : Sunday, March 30, 2025 at 08:04:34 PM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} \left (27 x^{2}+4\right ) y^{\prime \prime }+27 x y^{\prime }-3 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 29

ode:=(27*x^2+4)*diff(diff(y(x),x),x)+27*x*diff(y(x),x)-3*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \sinh \left (\frac {\operatorname {arcsinh}\left (\frac {3 \sqrt {3}\, x}{2}\right )}{3}\right )+c_2 \cosh \left (\frac {\operatorname {arcsinh}\left (\frac {3 \sqrt {3}\, x}{2}\right )}{3}\right ) \]

✓ Mathematica. Time used: 0.065 (sec). Leaf size: 47

ode=-3*y[x] + 27*x*D[y[x],x] + (4 + 27*x^2)*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_1 \cosh \left (\frac {1}{3} \text {arcsinh}\left (\frac {3 \sqrt {3} x}{2}\right )\right )+i c_2 \sinh \left (\frac {1}{3} \text {arcsinh}\left (\frac {3 \sqrt {3} x}{2}\right )\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(27*x*Derivative(y(x), x) + (27*x**2 + 4)*Derivative(y(x), (x, 2)) - 3*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False