83.21.3 problem 3

Internal problem ID [19176]
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 (D) at page 57
Problem number : 3
Date solved : Monday, March 31, 2025 at 06:51:15 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} y&=x y^{\prime }+a y^{\prime } \left (1-y^{\prime }\right ) \end{align*}

✓ Maple. Time used: 0.041 (sec). Leaf size: 29

ode:=y(x) = x*diff(y(x),x)+a*diff(y(x),x)*(1-diff(y(x),x)); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {\left (a +x \right )^{2}}{4 a} \\ y &= -c_1 \left (\left (c_1 -1\right ) a -x \right ) \\ \end{align*}

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 32

ode=y[x]==x*D[y[x],x]+a*D[y[x],x]*(1-D[y[x],x]); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to c_1 (a+a (-c_1)+x) \\ y(x)\to \frac {(a+x)^2}{4 a} \\ \end{align*}

✓ Sympy. Time used: 2.908 (sec). Leaf size: 435

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(-a*(1 - Derivative(y(x), x))*Derivative(y(x), x) - x*Derivative(y(x), x) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \text {Solution too large to show} \]