29.35.16 problem 1049

Internal problem ID [5614]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 35
Problem number : 1049
Date solved : Sunday, March 30, 2025 at 09:20:12 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 25

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

\begin{align*} y &= \frac {1}{-x +c_1} \\ y &= -x^{2}+c_1 \\ y &= c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.062 (sec). Leaf size: 31

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

\begin{align*} y(x)\to -\frac {1}{x+c_1} \\ y(x)\to c_1 \\ y(x)\to -x^2+c_1 \\ \end{align*}

✓ Sympy. Time used: 0.219 (sec). Leaf size: 19

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

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