60.3.168 problem 1182

Internal problem ID [11164]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1182
Date solved : Sunday, March 30, 2025 at 07:44:39 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 16

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

\[ y = x \left (\ln \left (x \right ) c_1 x +c_2 x +5\right ) \]

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 20

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

\[ y(x)\to x (c_1 x+2 c_2 x \log (x)+5) \]

✓ Sympy. Time used: 0.214 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = x \left (C_{1} x + C_{2} x \log {\left (x \right )} + 5\right ) \]