40.4.11 problem 19 (L)

Internal problem ID [6651]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 6. Equations of first order and first degree (Linear equations). Supplemetary problems. Page 39
Problem number : 19 (L)
Date solved : Sunday, March 30, 2025 at 11:13:40 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 29

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

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

✓ Mathematica. Time used: 1.873 (sec). Leaf size: 53

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

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

✓ Sympy. Time used: 0.693 (sec). Leaf size: 29

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

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