60.1.271 problem 277

Internal problem ID [10285]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 277
Date solved : Wednesday, March 05, 2025 at 10:00:29 AM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} \left (y^{2}+x^{4}\right ) y^{\prime }-4 x^{3} y&=0 \end{align*}

✓ Maple. Time used: 0.530 (sec). Leaf size: 41

ode:=(y(x)^2+x^4)*diff(y(x),x)-4*x^3*y(x) = 0; 
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: 0.297 (sec). Leaf size: 58

ode=(y[x]^2+x^4)*D[y[x],x]-4*x^3*y[x]==0; 
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: 0.774 (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)
 

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