82.12.32 problem Ex. 35

Internal problem ID [18726]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter II. Equations of the first order and of the first degree. Examples on chapter II at page 29
Problem number : Ex. 35
Date solved : Monday, March 31, 2025 at 06:03:06 PM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.251 (sec). Leaf size: 46

ode:=2*x^2*y(x)^2+y(x)-(x^3*y(x)-3*x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\operatorname {RootOf}\left (-4 \textit {\_Z}^{7} x^{2} \left (\frac {x}{c_1}\right )^{{6}/{7}}+\textit {\_Z}^{12} c_1^{2}+5 x^{2} \left (\frac {x}{c_1}\right )^{{6}/{7}}\right )^{7}}{x^{2}} \]

✓ Mathematica. Time used: 10.85 (sec). Leaf size: 997

ode=(2*x^2*y[x]^2+y[x])-(x^3*y[x]-3*x)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Sympy. Time used: 0.614 (sec). Leaf size: 31

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

\[ - \log {\left (x \right )} + \frac {3 \log {\left (x^{2} y{\left (x \right )} \right )}}{5} - \frac {7 \log {\left (x^{2} y{\left (x \right )} - \frac {5}{4} \right )}}{20} = C_{1} \]