15.7.20 problem 20

Internal problem ID [3001]
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 : 20
Date solved : Sunday, March 30, 2025 at 01:05:12 AM
CAS classification : [[_homogeneous, `class G`], _rational]

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

With initial conditions

\begin{align*} y \left (1\right )&=1 \end{align*}

✓ Maple. Time used: 0.506 (sec). Leaf size: 26

ode:=2*y(x) = (x^2*y(x)^4+x)*diff(y(x),x); 
ic:=y(1) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {100 x^{2}}{\operatorname {RootOf}\left (\textit {\_Z}^{9}-100000000 x^{9}-9 \textit {\_Z}^{8}\right )^{2}} \]

✓ Mathematica. Time used: 4.762 (sec). Leaf size: 33

ode=2*y[x]==(x^2*y[x]^4+x)*D[y[x],x]; 
ic={y[1]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \text {Root}\left [\text {$\#$1}^9 x^2+18 \text {$\#$1}^5 x+81 \text {$\#$1}-100 x^2\&,1\right ] \]

✓ Sympy. Time used: 0.525 (sec). Leaf size: 36

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-x**2*y(x)**4 - x)*Derivative(y(x), x) + 2*y(x),0) 
ics = {y(1): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ - \log {\left (x \right )} + \frac {4 \log {\left (\sqrt [4]{x} y{\left (x \right )} \right )}}{9} + \frac {8 \log {\left (x y^{4}{\left (x \right )} + 9 \right )}}{9} = \frac {8 \log {\left (10 \right )}}{9} \]