54.2.75 problem 651

Internal problem ID [11949]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 651
Date solved : Tuesday, September 30, 2025 at 11:46:55 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} y^{\prime }&=\frac {\left (\ln \left (y\right )+x^{2}\right ) y}{x} \end{align*}

✓ Maple. Time used: 0.030 (sec). Leaf size: 10

ode:=diff(y(x),x) = (ln(y(x))+x^2)*y(x)/x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{x \left (c_1 +x \right )} \]

✓ Mathematica. Time used: 0.169 (sec). Leaf size: 15

ode=D[y[x],x] == ((x^2 + Log[y[x]])*y[x])/x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{x (x+2 c_1)} \end{align*}

✓ Sympy. Time used: 0.410 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = e^{- x \left (- C_{1} - x\right )} \]