29.22.2 problem 608

Internal problem ID [5202]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 22
Problem number : 608
Date solved : Sunday, March 30, 2025 at 06:51:54 AM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} \left (x^{4}+y^{2}\right ) y^{\prime }&=4 x^{3} y \end{align*}

✓ Maple. Time used: 0.038 (sec). Leaf size: 41

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

\begin{align*} y &= \frac {\sqrt {4 x^{4}+c_1^{2}}}{2}+\frac {c_1}{2} \\ y &= -\frac {\sqrt {4 x^{4}+c_1^{2}}}{2}+\frac {c_1}{2} \\ \end{align*}

✓ Mathematica. Time used: 0.294 (sec). Leaf size: 58

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

\begin{align*} y(x)\to \frac {1}{2} \left (c_1-\sqrt {4 x^4+c_1{}^2}\right ) \\ y(x)\to \frac {1}{2} \left (\sqrt {4 x^4+c_1{}^2}+c_1\right ) \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.816 (sec). Leaf size: 34

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

\[ \left [ y{\left (x \right )} = 2 C_{1} - \sqrt {4 C_{1}^{2} + x^{4}}, \ y{\left (x \right )} = 2 C_{1} + \sqrt {4 C_{1}^{2} + x^{4}}\right ] \]