15.6.15 problem 15

Internal problem ID [2972]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 10, page 41
Problem number : 15
Date solved : Sunday, March 30, 2025 at 01:02:44 AM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

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

\[ x -\frac {y^{4}}{7}-\sqrt {y}\, c_1 = 0 \]

✓ Mathematica. Time used: 60.129 (sec). Leaf size: 257

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

\begin{align*} y(x)\to \text {Root}\left [\text {$\#$1}^8-14 \text {$\#$1}^4 x-49 \text {$\#$1} c_1{}^2+49 x^2\&,1\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^8-14 \text {$\#$1}^4 x-49 \text {$\#$1} c_1{}^2+49 x^2\&,2\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^8-14 \text {$\#$1}^4 x-49 \text {$\#$1} c_1{}^2+49 x^2\&,3\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^8-14 \text {$\#$1}^4 x-49 \text {$\#$1} c_1{}^2+49 x^2\&,4\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^8-14 \text {$\#$1}^4 x-49 \text {$\#$1} c_1{}^2+49 x^2\&,5\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^8-14 \text {$\#$1}^4 x-49 \text {$\#$1} c_1{}^2+49 x^2\&,6\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^8-14 \text {$\#$1}^4 x-49 \text {$\#$1} c_1{}^2+49 x^2\&,7\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^8-14 \text {$\#$1}^4 x-49 \text {$\#$1} c_1{}^2+49 x^2\&,8\right ] \\ \end{align*}

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - 2*y(x)/(x + y(x)**4) cannot be solved by the factorable group method