77.18.14 problem 14

Internal problem ID [20509]
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 : 14
Date solved : Thursday, October 02, 2025 at 06:03:42 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 37

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

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

✓ Mathematica. Time used: 0.05 (sec). Leaf size: 46

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

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

✓ Sympy. Time used: 0.180 (sec). Leaf size: 26

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

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