77.18.7 problem 7

Internal problem ID [20502]
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 : 7
Date solved : Thursday, October 02, 2025 at 06:03:38 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 23

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

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

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 30

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

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

✓ Sympy. Time used: 0.109 (sec). Leaf size: 19

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

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