54.3.171 problem 1185

Internal problem ID [12466]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1185
Date solved : Wednesday, October 01, 2025 at 01:45:26 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+5 x y^{\prime }-\left (2 x^{3}-4\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 33

ode:=x^2*diff(diff(y(x),x),x)+5*x*diff(y(x),x)-(2*x^3-4)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_2 \operatorname {BesselK}\left (0, \frac {2 \sqrt {2}\, x^{{3}/{2}}}{3}\right )+c_1 \operatorname {BesselI}\left (0, \frac {2 \sqrt {2}\, x^{{3}/{2}}}{3}\right )}{x^{2}} \]

✓ Mathematica. Time used: 0.04 (sec). Leaf size: 65

ode=(4 - 2*x^3)*y[x] + 5*x*D[y[x],x] + x^2*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {6 \sqrt [3]{3} c_2 K_0\left (\frac {2}{3} \sqrt {2} x^{3/2}\right )-3 \sqrt [3]{-3} c_1 \operatorname {BesselI}\left (0,\frac {2}{3} \sqrt {2} x^{3/2}\right )}{2^{2/3} x^2} \end{align*}

✓ Sympy. Time used: 0.154 (sec). Leaf size: 41

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + 5*x*Derivative(y(x), x) - (2*x**3 - 4)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} I_{0}\left (\frac {2 \sqrt {2} x^{\frac {3}{2}}}{3}\right ) + C_{2} Y_{0}\left (\frac {2 \sqrt {2} i x^{\frac {3}{2}}}{3}\right )}{x^{2}} \]