29.13.15 problem 369

Internal problem ID [4969]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 13
Problem number : 369
Date solved : Sunday, March 30, 2025 at 04:26:57 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

\begin{align*} x^{4} y^{\prime }&=\left (x^{3}+y\right ) y \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 19

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

\[ y = \frac {2 x^{3}}{2 c_1 \,x^{2}+1} \]

✓ Mathematica. Time used: 0.163 (sec). Leaf size: 26

ode=x^4 D[y[x],x]==(x^3+y[x])y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {2 x^3}{1+2 c_1 x^2} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.203 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = \frac {2 x^{3}}{C_{1} x^{2} + 1} \]