54.1.203 problem 207

Internal problem ID [11517]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 207
Date solved : Tuesday, September 30, 2025 at 08:56:12 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

\begin{align*} y y^{\prime }+y^{2}+4 x \left (x +1\right )&=0 \end{align*}

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

ode:=y(x)*diff(y(x),x)+y(x)^2+4*x*(1+x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 4.242 (sec). Leaf size: 47

ode=y[x]*D[y[x],x]+y[x]^2+4*x*(x+1)==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.358 (sec). Leaf size: 36

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x*(x + 1) + y(x)**2 + y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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