54.1.206 problem 210

Internal problem ID [11520]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 210
Date solved : Tuesday, September 30, 2025 at 08:56:18 PM
CAS classification : [_separable]

\begin{align*} y y^{\prime }+x y^{2}-4 x&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 33

ode:=y(x)*diff(y(x),x)+x*y(x)^2-4*x = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \sqrt {{\mathrm e}^{-x^{2}} c_1 +4} \\ y &= -\sqrt {{\mathrm e}^{-x^{2}} c_1 +4} \\ \end{align*}

✓ Mathematica. Time used: 1.817 (sec). Leaf size: 57

ode=y[x]*D[y[x],x]+x*y[x]^2-4*x==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\sqrt {4+e^{-x^2+2 c_1}}\\ y(x)&\to \sqrt {4+e^{-x^2+2 c_1}}\\ y(x)&\to -2\\ y(x)&\to 2 \end{align*}

✓ Sympy. Time used: 0.366 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*y(x)**2 - 4*x + y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \sqrt {C_{1} e^{- x^{2}} + 4}, \ y{\left (x \right )} = \sqrt {C_{1} e^{- x^{2}} + 4}\right ] \]