83.18.17 problem 17

Internal problem ID [19148]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter IV. Equations of the first order but not of the first degree. Exercise IV (A) at page 53
Problem number : 17
Date solved : Thursday, March 13, 2025 at 01:45:43 PM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{3}+2 x {y^{\prime }}^{2}-y^{2} {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*diff(y(x),x)^2-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 \left (x \right ) &= \frac {1}{-x +c_{1}} \\ y \left (x \right ) &= -x^{2}+c_{1} \\ y \left (x \right ) &= c_{1} \\ \end{align*}

✓ Mathematica. Time used: 0.057 (sec). Leaf size: 31

ode=D[y[x],x]^3+2*x*D[y[x],x]^2-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: 0.208 (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*Derivative(y(x), x)**2 - y(x)**2*Derivative(y(x), x)**2 + Derivative(y(x), x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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