34.3.16 problem 25 (a)

Internal problem ID [7907]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary problems. Page 33
Problem number : 25 (a)
Date solved : Tuesday, September 30, 2025 at 05:09:56 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

\begin{align*} x -x^{2}-y^{2}+y y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 37

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

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

✓ Mathematica. Time used: 3.578 (sec). Leaf size: 47

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

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

✓ Sympy. Time used: 0.326 (sec). Leaf size: 32

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

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