23.1.361 problem 346

Internal problem ID [4968]
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 : 346
Date solved : Tuesday, September 30, 2025 at 09:06:29 AM
CAS classification : [_linear]

\begin{align*} x^{3} y^{\prime }&=a +b \,x^{2} y \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 21

ode:=x^3*diff(y(x),x) = a+b*x^2*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {a}{\left (2+b \right ) x^{2}}+x^{b} c_1 \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 23

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

\begin{align*} y(x)&\to -\frac {a}{(b+2) x^2}+c_1 x^b \end{align*}

✓ Sympy. Time used: 0.277 (sec). Leaf size: 26

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

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