75.6.24 problem 157

Internal problem ID [16701]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page 54
Problem number : 157
Date solved : Thursday, March 13, 2025 at 08:32:26 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 14

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

\[ y = \frac {1}{{\mathrm e}^{x^{2}} c_{1} +1} \]

✓ Mathematica. Time used: 0.262 (sec). Leaf size: 42

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

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[1]-1) K[1]}dK[1]\&\right ]\left [x^2+c_1\right ] \\ y(x)\to 0 \\ y(x)\to 1 \\ \end{align*}

✓ Sympy. Time used: 0.389 (sec). Leaf size: 12

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

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