73.7.36 problem 36

Internal problem ID [15115]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 36
Date solved : Thursday, March 13, 2025 at 05:40:45 AM
CAS classification : [[_homogeneous, `class G`], _exact, _rational]

\begin{align*} x y^{2}+\left (x^{2} y+10 y^{4}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 24

ode:=x*y(x)^2+(x^2*y(x)+10*y(x)^4)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= 0 \\ \frac {x^{2} y^{2}}{2}+2 y^{5}+c_{1} &= 0 \\ \end{align*}

✓ Mathematica. Time used: 3.908 (sec). Leaf size: 141

ode=x*y[x]^2+(x^2*y[x]+10*y[x]^4)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to 0 \\ y(x)\to \text {Root}\left [4 \text {$\#$1}^5+\text {$\#$1}^2 x^2-2 c_1\&,1\right ] \\ y(x)\to \text {Root}\left [4 \text {$\#$1}^5+\text {$\#$1}^2 x^2-2 c_1\&,2\right ] \\ y(x)\to \text {Root}\left [4 \text {$\#$1}^5+\text {$\#$1}^2 x^2-2 c_1\&,3\right ] \\ y(x)\to \text {Root}\left [4 \text {$\#$1}^5+\text {$\#$1}^2 x^2-2 c_1\&,4\right ] \\ y(x)\to \text {Root}\left [4 \text {$\#$1}^5+\text {$\#$1}^2 x^2-2 c_1\&,5\right ] \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 5.252 (sec). Leaf size: 3

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*y(x)**2 + (x**2*y(x) + 10*y(x)**4)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 0 \]