23.1.358 problem 343

Internal problem ID [4965]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 343
Date solved : Tuesday, September 30, 2025 at 09:06:15 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.009 (sec). Leaf size: 24

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

\[ y = {\mathrm e}^{{\mathrm e}^{c c_1} \left (b \,x^{2}+a \right )^{\frac {c}{2 b}}} \]

✓ Mathematica. Time used: 0.221 (sec). Leaf size: 33

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

\begin{align*} y(x)&\to e^{e^{c_1} \left (a+b x^2\right )^{\frac {c}{2 b}}}\\ y(x)&\to 1 \end{align*}

✓ Sympy. Time used: 0.375 (sec). Leaf size: 20

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

\[ y{\left (x \right )} = e^{C_{1} e^{\frac {c \log {\left (a + b x^{2} \right )}}{2 b}}} \]