15.7.13 problem 13

Internal problem ID [2994]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 11, page 45
Problem number : 13
Date solved : Sunday, March 30, 2025 at 01:04:04 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} x y^{\prime }+2 y&=3 x^{3} y^{{4}/{3}} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

ode:=x*diff(y(x),x)+2*y(x) = 3*x^3*y(x)^(4/3); 
dsolve(ode,y(x), singsol=all);
 

\[ \frac {1}{y^{{1}/{3}}}+\frac {3 x^{3}}{7}-x^{{2}/{3}} c_1 = 0 \]

✓ Mathematica. Time used: 0.185 (sec). Leaf size: 29

ode=x*D[y[x],x]+2*y[x]==3*x^3*y[x]^(4/3); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\frac {343}{x^2 \left (3 x^{7/3}-7 c_1\right ){}^3} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.340 (sec). Leaf size: 36

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*x**3*y(x)**(4/3) + x*Derivative(y(x), x) + 2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {343}{343 C_{1}^{3} x^{2} - 441 C_{1}^{2} x^{\frac {13}{3}} + 189 C_{1} x^{\frac {20}{3}} - 27 x^{9}} \]