73.4.2 problem 5.1 (b)

Internal problem ID [15013]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 5. LINEAR FIRST ORDER EQUATIONS. Additional exercises. page 103
Problem number : 5.1 (b)
Date solved : Monday, March 31, 2025 at 01:12:20 PM
CAS classification : [`y=_G(x,y')`]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

NotImplementedError : The given ODE -(-3*x**2*y(x) + sin(x))/y(x)**2 + Derivative(y(x), x) cannot be solved by the factorable group method